share/contrib/diffequations/rtest_odelin.mac

   1 (kill(all), load(odelin), 0);
   2 0$
   3
   4 odelin(y+'diff(y,x,2),y,x);
   5 set(%e^-(%i*x),%e^(%i*x))$
   6
   7 odelin('diff(y,x)+'diff(y,x,2),y,x);
   8 set(1,%e^-x)$
   9
  10 (assume(notequal(b,a)), odelin(a*b*y+(-b-a+1)*x*'diff(y,x)+x^2*'diff(y,x,2),y,x));
  11 set(x^a,x^b)$
  12
  13 (forget(notequal(b,a)),0);
  14 0$
  15
  16 odelin(2*y+9*x^2*'diff(y,x)+9*x^2*'diff(y,x,2),y,x);
  17 set(bessel_j(1/6,-%i*x/2)*sqrt(-x)*%e^-(x/2),bessel_y(1/6,-%i*x/2)*sqrt(-x)*%e^-(x/2))$
  18
  19 odelin(-y+3*(x-1)*'diff(y,x)+2*x*(x-1)*'diff(y,x,2),y,x);
  20 set((x-1)/sqrt(x), (log(sqrt(x)+1)*x-log(sqrt(x)-1)*x-2*sqrt(x)-log(sqrt(x)+1) +log(sqrt(x)-1)) /sqrt(x))$
  21
  22 odelin(x^2*y+x*'diff(y,x)+x^2*'diff(y,x,2),y,x);
  23 set(bessel_j(0,-x),bessel_y(0,-x))$
  24
  25 odelin(-4*y+'diff(y,x)+x*'diff(y,x,2),y,x);
  26 set(bessel_j(0,4*sqrt(-x)), bessel_y(0,4*sqrt(-x)))$
  27
  28 odelin(y+(x+x^2)*'diff(y,x)+x^2*'diff(y,x,2),y,x);
  29 set(kummer_m(%i,2*%i+1,-x)*x^%i,kummer_u(%i,2*%i+1,-x)*x^%i)$
  30
  31 odelin(-y+(2-x)*'diff(y,x)+3*x*'diff(y,x,2),y,x);
  32 set(x^(1/3)*%e^(x/3),gamma_incomplete(-1/3,x/3)*x^(1/3)*%e^(x/3))$
  33
  34 odelin(-(3+x)*y+2*x^2*'diff(y,x)+4*x^2*'diff(y,x,2),y,x);
  35 set((x-2)/sqrt(x),%e^-(x/2)/sqrt(x))$
  36
  37 odelin(y+(x^2-x)*'diff(y,x)+x^2*'diff(y,x,2),y,x); /* 13 */
  38 set(x*%e^-x,gamma_incomplete(0,-x)*x*%e^-x)$
  39
  40 odelin(-x*y-'diff(y,x)+x*'diff(y,x,2),y,x);
  41 set(bessel_j(1,-%i*x)*x,bessel_y(1,-%i*x)*x)$
  42
  43 odelin((x-2)*y+8*x*'diff(y,x)+3*x^2*'diff(y,x,2),y,x);
  44 set(bessel_j(-7/3,2*sqrt(x)/sqrt(3))/x^(5/6), bessel_y(-7/3,2*sqrt(x)/sqrt(3))/x^(5/6))$
  45
  46 odelin(-2*y+(x-1)*'diff(y,x)+x*'diff(y,x,2),y,x);
  47 set(x^2,gamma_incomplete(-2,x)*x^2)$
  48
  49 odelin(-4*y+(5+x)*'diff(y,x)+x*(1+x)*'diff(y,x,2),y,x);
  50 set(gauss_a(-6,-2,-3,-x)/x^4,gauss_b(-6,-2,-3,-x)/x^4)$
  51
  52 odelin(-y+(1-x)*'diff(y,x)+x*'diff(y,x,2),y,x);
  53 set(%e^x,gamma_incomplete(0,x)*%e^x)$
  54
  55 odelin(y-x*(x+1)*'diff(y,x)+x^2*'diff(y,x,2),y,x);
  56 set(x*%e^x,gamma_incomplete(0,x)*x*%e^x)$
  57
  58 odelin(-4*y+2*(1-x)*'diff(y,x)+3*x*'diff(y,x,2),y,x);
  59 set(kummer_m(-1,4/3,-2*x/3)*x^(1/3)*%e^(2*x/3),kummer_u(-1,4/3,-2*x/3)*x^(1/3)*%e^(2*x/3))$
  60
  61 odelin(-y+(2+x)*'diff(y,x)+x*'diff(y,x,2),y,x);
  62 set(kummer_m(-2,0,-x)/x,kummer_u(-2,0,-x)/x)$
  63
  64 odelin(-2*y+(1/2-4*x)*'diff(y,x)+x*(1-x)*'diff(y,x,2),y,x); /* 22 */
  65 set(sqrt(x)/(x-1)^(5/2), (2*sqrt(x-1)*x-3*log(sqrt(x)+sqrt(x-1))*sqrt(x) +3*log(sqrt(x-1)-sqrt(x))*sqrt(x)+4*sqrt(x-1)) /(x-1)^(5/2))$
  66
  67 odelin(-45*y+(1-27*x)*'diff(y,x)+3*x*(1-x)*'diff(y,x,2),y,x);
  68 set(gauss_a(-4,-2,5/3,x)*x^(2/3)/(x-1)^(23/3),gauss_b(-4,-2,5/3,x)*x^(2/3)/(x-1)^(23/3))$
  69
  70 odelin(-2*y+(1-6*x)*'diff(y,x)+2*x*(1-x)*'diff(y,x,2),y,x);
  71 set((log(sqrt(x)+sqrt(x-1))*sqrt(x)-log(sqrt(x-1)-sqrt(x))*sqrt(x) -2*sqrt(x-1)) /(x-1)^(3/2),sqrt(x)/(x-1)^(3/2))$
  72
  73 odelin(-6*y+(3-10*x)*'diff(y,x)+2*x*(1-x)*'diff(y,x,2),y,x);
  74 set(1/((x-1)^(5/2)*sqrt(x)), (4*sqrt(x-1)*x^(3/2)-10*sqrt(x-1)*sqrt(x)+3*log(sqrt(x)+sqrt(x-1)) -3*log(sqrt(x-1)-sqrt(x))) /((x-1)^(5/2)*sqrt(x)))$
  75
  76 odelin(-y+(1-3*x)*'diff(y,x)+x*(1-x)*'diff(y,x,2),y,x);
  77 set(1/(x-1),log(x)/(x-1))$
  78
  79 odelin((-y)/4+(2-2*x)*'diff(y,x)+x*(1-x)*'diff(y,x,2),y,x);
  80 set(gauss_a(-1/2,-1/2,0,x)/x,gauss_b(-1/2,-1/2,0,x)/x)$
  81
  82
  83 odelin((4*x^2-1)*y+4*x*'diff(y,x)+4*x^2*'diff(y,x,2),y,x);
  84 set(%e^-(%i*x)/sqrt(x),%e^(%i*x)/sqrt(x))$
  85
  86 odelin((9*x^2-16)*y+9*x*'diff(y,x)+9*x^2*'diff(y,x,2),y,x);
  87 set(bessel_j(-4/3,-x),bessel_y(-4/3,-x))$
  88
  89 odelin((x^2-1)*y+x*'diff(y,x)+x^2*'diff(y,x,2),y,x);
  90 set(bessel_j(1,-x),bessel_y(1,-x))$
  91
  92 odelin(x^2*y+x*'diff(y,x)+x^2*'diff(y,x,2),y,x);
  93 set(bessel_j(0,-x), bessel_y(0,-x))$
  94
  95 odelin((9*x^2-4)*y+9*x*'diff(y,x)+9*x^2*'diff(y,x,2),y,x);
  96 set(bessel_j(-2/3,-x), bessel_y(-2/3,-x))$
  97
  98 odelin((x^2-16)*y+x*'diff(y,x)+x^2*'diff(y,x,2),y,x);
  99 set(bessel_j(4,-x), bessel_y(4,-x))$
 100
 101 odelin((x^2-1)*y+x*'diff(y,x)+x^2*'diff(y,x,2),y,x);
 102 set(bessel_j(1,-x), bessel_y(1,-x))$
 103
 104 odelin((x^2-4)*y+x*'diff(y,x)+x^2*'diff(y,x,2),y,x);
 105 set(bessel_j(2,-x), bessel_y(2,-x))$
 106
 107 odelin(6*y+5*'diff(y,x)+'diff(y,x,2),y,x);
 108 set(%e^-(3*x),%e^-(2*x))$
 109
 110 odelin(16*y+8*'diff(y,x)+'diff(y,x,2),y,x);
 111 set(%e^-(4*x),x*%e^-(4*x))$
 112
 113 odelin(-y+'diff(y,x)+'diff(y,x,2),y,x);
 114 set(%e^(-sqrt(5)*x/2-x/2),%e^(sqrt(5)*x/2-x/2))$
 115
 116 odelin(-4*y+7*'diff(y,x)+2*'diff(y,x,2),y,x);
 117 set(%e^-(4*x),%e^(x/2))$
 118
 119 odelin(-11*y-'diff(y,x)+'diff(y,x,2),y,x);
 120 set(%e^(x/2-3*sqrt(5)*x/2),%e^(3*sqrt(5)*x/2+x/2))$
 121
 122 odelin(25*y+20*'diff(y,x)+4*'diff(y,x,2),y,x);
 123 set(%e^-(5*x/2),x*%e^-(5*x/2))$
 124
 125 odelin(7*y-8*'diff(y,x)+'diff(y,x,2),y,x);
 126 set(%e^x,%e^(7*x))$
 127
 128 odelin(8*y+4*'diff(y,x)+'diff(y,x,2),y,x);
 129 set(%e^(-2*%i*x-2*x),%e^(2*%i*x-2*x))$
 130
 131 odelin(25*y+10*'diff(y,x)+'diff(y,x,2),y,x);
 132 set(%e^-(5*x),x*%e^-(5*x))$
 133
 134 odelin(7*y+'diff(y,x,2),y,x);
 135 set(%e^-(sqrt(7)*%i*x),%e^(sqrt(7)*%i*x))$
 136
 137 odelin(5*y+2*'diff(y,x)+'diff(y,x,2),y,x);
 138 set(%e^(-2*%i*x-x),%e^(2*%i*x-x))$
 139
 140 odelin(26*y-2*'diff(y,x)+'diff(y,x,2),y,x);
 141 set(%e^(x-5*%i*x),%e^(5*%i*x+x))$
 142
 143 odelin(6*y+6*x*'diff(y,x)+x^2*'diff(y,x,2),y,x);
 144 set(1/x^3,1/x^2)$
 145
 146 odelin(15*y+13*x*'diff(y,x)+2*x^2*'diff(y,x,2),y,x);
 147 set(1/x^3,1/x^(5/2))$
 148
 149 odelin(17*y-x*'diff(y,x)+x^2*'diff(y,x,2),y,x);
 150 set(x^(1-4*%i),x^(4*%i+1))$
 151
 152 odelin(-3*y+2*'diff(y,x)+x^2*'diff(y,x,2),y,x);
 153 set(kummer_m((sqrt(13)+3)/2,sqrt(13)+1,-2/x) *(x)^(-sqrt(13)/2-1/2)*%e^(2/x)*abs(x), kummer_u((sqrt(13)+3)/2,
 154     sqrt(13)+1,-2/x) *(x)^(-sqrt(13)/2-1/2)*%e^(2/x)*abs(x))$
 155
 156 odelin(-(3+x)*y+2*x^2*'diff(y,x)+4*x^2*'diff(y,x,2),y,x);
 157 set((x-2)/sqrt(x),%e^-(x/2)/sqrt(x))$
 158
 159 odelin(y+(x^2-x)*'diff(y,x)+x^2*'diff(y,x,2),y,x);
 160 set(x*%e^-x,gamma_incomplete(0,-x)*x*%e^-x)$
 161
 162 odelin(-x*y-'diff(y,x)+x*'diff(y,x,2),y,x);
 163 set(bessel_j(1,-%i*x)*x, bessel_y(1,-%i*x)*x)$
 164
 165 odelin((x-2)*y+8*x*'diff(y,x)+3*x^2*'diff(y,x,2),y,x);
 166 set(bessel_j(-7/3,2*sqrt(x)/sqrt(3))/x^(5/6), bessel_y(-7/3,2*sqrt(x)/sqrt(3))/x^(5/6))$
 167
 168 odelin(-2*y+(x-1)*'diff(y,x)+x*'diff(y,x,2),y,x);
 169 set(x^2,gamma_incomplete(-2,x)*x^2)$
 170
 171 odelin(-4*y+(5+x)*'diff(y,x)+x*(1+x)*'diff(y,x,2),y,x);
 172 set(gauss_a(-6,-2,-3,-x)/x^4,gauss_b(-6,-2,-3,-x)/x^4)$
 173
 174 odelin(-y+(1-x)*'diff(y,x)+x*'diff(y,x,2),y,x);
 175 set(%e^x,gamma_incomplete(0,x)*%e^x)$
 176
 177 odelin(y-x*(x+1)*'diff(y,x)+x^2*'diff(y,x,2),y,x);
 178 set(x*%e^x,gamma_incomplete(0,x)*x*%e^x)$
 179
 180 odelin(-y+2*(1-x)*'diff(y,x)+3*x*'diff(y,x,2),y,x);
 181 set(kummer_m(1/2,4/3,-2*x/3)*x^(1/3)*%e^(2*x/3),
 182         kummer_u(1/2,4/3,-2*x/3)*x^(1/3)*%e^(2*x/3))$
 183
 184 (assume(2*n-b > 0, 2*n+b>0),0);
 185 0$
 186
 187 odelin((b^2-(4*n^2-1))*y/(4*x^2)+'diff(y,x,2),y,x);
 188 set(x^(1/2-sqrt(2*n-b)*sqrt(2*n+b)/2),x^(sqrt(2*n-b)*sqrt(2*n+b)/2+1/2))$
 189
 190 (forget(2*n-b>0, 2*n+b>0),0);
 191 0$
 192
 193 odelin(((a^2-n^2)/x^2+b^2)*y+(1-2*a)*'diff(y,x)/x+'diff(y,x,2),y,x);
 194 set(bessel_j(n,-b*x)*x^a, bessel_y(n,-b*x)*x^a)$
 195
 196 odelin(b^2*x^3*y+'diff(y,x,2),y,x);
 197 set(bessel_j(-1/5,2*abs(b)*x^(5/2)/5)*sqrt(x), bessel_y(-1/5,2*abs(b)*x^(5/2)/5)*sqrt(x))$
 198
 199 odelin(b^2*x^2*y+'diff(y,x,2),y,x);
 200 set(bessel_j(-1/4,-b*x^2/2)*abs(x)/sqrt(-x), bessel_y(-1/4,-b*x^2/2)*abs(x)/sqrt(-x))$
 201
 202 odelin(4*(x^2-n^2/x^2)*y+'diff(y,x)/x+'diff(y,x,2),y,x);
 203 set(bessel_j(n,x^2)*abs(x)/x,bessel_y(n,x^2)*abs(x)/x)$
 204
 205 odelin((1-n^2/x)*y/(4*x)+'diff(y,x)/x+'diff(y,x,2),y,x);
 206 set(bessel_j(n,sqrt(x)), bessel_y(n,sqrt(x)))$
 207
 208 odelin(y/(4*x)+(1-n)*'diff(y,x)/x+'diff(y,x,2),y,x);
 209 set(bessel_j(n,sqrt(x))*x^(n/2), bessel_y(n,sqrt(x))*x^(n/2))$
 210
 211
 212 odelin(('diff(y,x,1) = (-((-96*x^3-200*x^5-100*x^7)*y
 213                     +(x+4*x^3+6*x^5+4*x^7+x^9)*'diff(y,x,2)))
 214                     /(-1-2*x^2+2*x^6+x^8)),y,x);
 215 set(-bessel_j(5,-1/(x^2+1)),-bessel_y(5,-1/(x^2+1)))$
 216
 217
 218 odelin(('diff(y,x,2) = (-((x+3*x^3+3*x^5+x^7)*y
 219                     +(1-7*x^2+14*x^4-10*x^6+x^8+x^10)*'diff(y,x,1)))
 220                     /(x-3*x^3+2*x^5+2*x^7-3*x^9+x^11)),y,x);
 221 set(bessel_j(0,-x/(x^2-1)), bessel_y(0,-x/(x^2-1)))$
 222
 223 odelin(('diff(y,x,2) = (-((-x+3*x^3-3*x^5+x^7)*y
 224                     +(-1-5*x-16*x^2-31*x^3-43*x^4-40*x^5-25*x^6-7*x^7+2*x^8
 225                         +3*x^9+x^10)
 226                      *'diff(y,x,1)))
 227                     /(-x-4*x^2-9*x^3-12*x^4-9*x^5+9*x^7+12*x^8+9*x^9+4*x^10
 228                         +x^11)),y,x);
 229 set(bessel_j(0,-x/(x^2+x+1)), bessel_y(0,-x/(x^2+x+1)))$
 230
 231 odelin(('diff(y,x,2) = (2*x*'diff(y,x,1)-2*y)/x^2),y,x);
 232 set(x,x^2)$
 233
 234 odelin(('diff(y,x,2) = (-((-4+5*x-x^2)*y+(4*x-5*x^2+x^3)*'diff(y,x,1)))/(x^3-2*x^2)),y,x);
 235 set(x,(x-1)*x*%e^-x)$
 236
 237 odelin(('diff(y,x,2) = ((1+4*x-8*x^2+4*x^3-x^4)*y
 238                     +(-x-4*x^2+8*x^3-4*x^4+x^5)*'diff(y,x,1))
 239                     /(-1+x-4*x^2+2*x^3-3*x^4+x^5)),y,x);
 240 set(x,%e^x/(x^2+1))$
 241
 242 odelin(('diff(y,x,2) = ((-6+2*b+(24-a-8*b)*x+(-26+6*a+8*b)*x^2+(16-12*a)*x^3 +(8*a-8)*x^4) *y
 243       +((4-b)*x+(4*b-15)*x^2+(15-4*b)*x^3-8*x^4+4*x^5) *'diff(y,x,1)) /(x^2-3*x^3+2*x^4)),y,x);
 244 set(kummer_m(a,b,(x-1)*x)*x^2,kummer_u(a,b,(x-1)*x)*x^2)$
 245
 246
 247 odelin(('diff(y,x,2) = ((-a^2+6*a^2*x-12*a^2*x^2+8*a^2*x^3)*y +(-1+(4-3*a)*x+
 248         (7*a-4)*x^2-8*a*x^3+4*a*x^4)*'diff(y,x,1)) /(a*x-3*a*x^2+2*a*x^3)),y,x);
 249
 250 set(kummer_m(a,1/a,(x-1)*x),kummer_u(a,1/a,(x-1)*x))$
 251
 252 odelin(('diff(y,x,2) = ((a+6*a*x+12*a*x^2+8*a*x^3)*y
 253                     +(-1+2*a+(12*a-11)*x+(30*a-27)*x^2+(44*a-38)*x^3
 254                         +(42*a-34)*x^4+(24*a-18)*x^5+(8*a-6)*x^6)
 255                      *'diff(y,x,1))
 256                     /(1+5*x+12*x^2+19*x^3+20*x^4+15*x^5+7*x^6+2*x^7)),y,x);
 257 set(bessel_j(-((2*a-1)/2),-(%i/(2*(x^2+x+1))))*(x^2+x+1)^(a-1/2) *%e^(1/(2*x^2+2*x+2)),
 258   bessel_y(-((2*a-1)/2),-(%i/(2*(x^2+x+1))))*(x^2+x+1)^(a-1/2) *%e^(1/(2*x^2+2*x+2)))$
 259
 260 odelin(('diff(y,x,2) = (-(n*u*y+((1+n+u)*x-k)*'diff(y,x,1)))/(x^2-x)),y,x);
 261 set(gauss_a(n,u,k,x),gauss_b(n,u,k,x))$
 262
 263 odelin(('diff(y,x,2) = (-(n*u*y+(-15+3*k-15*n-15*u+(1+n+u)*x)*'diff(y,x,1))) /(180-27*x+x^2)),y,x);
 264 set(gauss_a(n,u,u+n-k+1,(x-12)/3),gauss_b(n,u,u+n-k+1,(x-12)/3))$
 265
 266 odelin(('diff(y,x,2) = (-((-n*u+(-1+n+u)*x+(1-k)*x^2+x^3)*y
 267      +((-1+n+u)*x-k*x^2+2*x^3)*'diff(y,x,1)))/(x^3-x^2)),y,x);
 268 set(gauss_a(n-k+1,n,-u+n+1,x)*x^n*%e^-x,
 269         gauss_b(n-k+1,n,-u+n+1,x)*x^n*%e^-x)$
 270
 271
 272 odelin(('diff(y,x,2) = (-((-304+115*x-60*x^2+9*x^3)*y
 273                     +(96*x-69*x^2+18*x^3)*'diff(y,x,1)))
 274                     /(9*x^3-9*x^2)),y,x)$
 275 set(x^(19/3)*%e^-x,
 276   x^(16/3)*%e^-x *(60*x^5*log(x)-240*x^4*log(x)+360*x^3*log(x)-240*x^2*log(x) +60*x*log(x)
 277     -60*x^5*log(x-1)+240*x^4*log(x-1) -360*x^3*log(x-1)+240*x^2*log(x-1)-60*x*log(x-1)
 278     -60*x^4+210*x^3-260*x^2+125*x-12) /(x-1)^4)$
 279
 280 odelin(('diff(y,x,2) = (-((-30+180*x-360*x^2+240*x^3)*y
 281                     +(-7+14*x+32*x^2-92*x^3+46*x^4)*'diff(y,x,1)))
 282                     /(-x+2*x^2+2*x^3-5*x^4+2*x^5)),y,x);
 283 set(1/((x-1)^6*x^6), (60*x^8*log(x^2-x-1)-240*x^7*log(x^2-x-1)+120*x^6*log(x^2-x-1)
 284     +480*x^5*log(x^2-x-1)-300*x^4*log(x^2-x-1) -480*x^3*log(x^2-x-1)+120*x^2*log(x^2-x-1)
 285     +240*x*log(x^2-x-1)+60*log(x^2-x-1)+12*x^10-60*x^9+72*x^8 +72*x^7-276*x^6+324*x^5+60*x^4
 286     -456*x^3+4*x^2+248*x+77) /((x-1)^6*x^6*(x^2-x-1)^4))$
 287
 288 odelin(('diff(y,x,2) = (30*y+(15-20*x+5*x^2)*'diff(y,x,1))/(-2+5*x-4*x^2+x^3)),y,x);
 289 set((x-1)^6, (x-1)^5*(60*x^5*log(x-1)-540*x^4*log(x-1)+1920*x^3*log(x-1)-3360*x^2*log(x-1)
 290     +2880*x*log(x-1)-960*log(x-1)-60*x^5*log(x-2) +540*x^4*log(x-2)-1920*x^3*log(x-2)
 291     +3360*x^2*log(x-2) -2880*x*log(x-2)+960*log(x-2)-60*x^4+450*x^3-1250*x^2 +1515*x-667) /(x-2)^4)$
 292
 293 odelin(('diff(y,x,2) = (-((a^2+a*b)*y+(-8-2*a-b+(1+2*a+b)*x)*'diff(y,x,1)))
 294                     /(2-3*x+x^2)),y,x)$
 295 set(gauss_a(a,b+a,7,x-1),gauss_b(a,b+a,7,x-1))$
 296
 297
 298 odelin(('diff(y,x,2) = (-((a^2+6*a^2*x+12*a^2*x^2+8*a^2*x^3)*y
 299                     +(1+a+(3+6*a)*x+(5+14*a)*x^2+(4+16*a)*x^3+(2+8*a)*x^4)
 300                      *'diff(y,x,1)))
 301                     /(x+4*x^2+6*x^3+5*x^4+2*x^5)),y,x);
 302 set(1/(x^a*(x+1)^a), ('integrate(x^(a-1)*(x+1)^(a-1)*(2*x+1)/(x^2+x+1)^a,x))/(x^a*(x+1)^a))$
 303
 304 odelin(('diff(y,x,2) = (-((2*x^2-1)*y+8*x*'diff(y,x,1)))/(2*x^2-2)),y,x);
 305 set(spherodialwave_a(1,1/2,1/4,-x),spherodialwave_b(1,1/2,1/4,-x))$
 306
 307 odelin(('diff(y,x,2) = (-((6*x^2-28)*y+(6*x^3+2*x^5)*'diff(y,x,1)))/(x^6-x^4)),y,x);
 308 set(spherodialwave_a(-3,12,7,-(1/x))*x^5*abs(x)/((x-1)^3*(x+1)^3),
 309   spherodialwave_b(-3,12,7,-(1/x))*x^5*abs(x)/((x-1)^3*(x+1)^3))$
 310
 311 odelin(('diff(y,x,2) = (-((-22-12*x+6*x^2)*y
 312                     +(-8+28*x-38*x^2+26*x^3-10*x^4+2*x^5)*'diff(y,x,1)))
 313                     /(-2*x+9*x^2-16*x^3+14*x^4-6*x^5+x^6)),y,x);
 314 set(spherodialwave_a(-3,12,7,-1/(x-1))*(x-1)^6/((x-2)^3*x^3),
 315   spherodialwave_b(-3,12,7,-1/(x-1))*(x-1)^6/((x-2)^3*x^3))$
 316
 317 odelin(('diff(y,x,2) = (-((784-4703*x+9401*x^2-6254*x^3-20*x^4+8*x^5)*y
 318                     +(-4*x+12*x^2-16*x^3+8*x^4)*'diff(y,x,1)))
 319                     /(-4*x^2+16*x^3-20*x^4+8*x^5)),y,x);
 320 set(bessel_j(28,sqrt(x-1)*sqrt(x)),bessel_y(28,sqrt(x-1)*sqrt(x)))$
 321
 322 odelin(('diff(y,x,2) = (-(2-933156*x)*y-x^2*'diff(y,x,1))/x^3),y,x);
 323 set(bessel_j(1932,2^(3/2)/sqrt(x))*abs(x)/x, bessel_y(1932,2^(3/2)/sqrt(x))*abs(x)/x)$
 324
 325 odelin(('diff(y,x,2) = (-1+x-x^2-4*x^3+x^4-x^5+x^6)*'diff(y,x,1)/(x^6-x^2)),y,x);
 326 set(1,'integrate((x^2+1)*%e^(x-1/x)/(x*(x^2-1)),x))$
 327
 328 odelin(('diff(y,x,2) = ((1+3*x^2+3*x^4+x^6)*y
 329                     +(-x-x^3-6*x^4+x^5-2*x^6+x^7)*'diff(y,x,1))
 330                     /(x^7-x^3)),y,x);
 331 set(x/((x-1)*(x+1)),x*%e^(x-1/x)/((x-1)*(x+1)))$
 332
 333 odelin(('diff(y,x,2) = ((2+6*x^2+6*x^4+2*x^6)*y
 334                     +(-2*x+3*x^2-2*x^3-6*x^4+2*x^5-x^6+2*x^7)*'diff(y,x,1))
 335                     /(2*x^7-2*x^3)),y,x);
 336 set(sqrt(x-1)*sqrt(x+1)*%e^(x-1/x)/sqrt(x), sqrt(x-1)*sqrt(x+1)*%e^(x-1/x) *('integrate((x^2+1)*%e^(1/x-x) /(sqrt(x-1)*sqrt(x)*sqrt(x+1)*(x^2-1)),x)) /sqrt(x))$
 337
 338 odelin(('diff(y,x,2) = (-(a^2*y-2*a^2*x*y+6*a*x^2*y-4*x^3*y+a^2*'diff(y,x,1)
 339                               +4*a^2*x^2*'diff(y,x,1)-8*a*x^3*'diff(y,x,1)
 340                               +4*x^4*'diff(y,x,1)))
 341                     /(2*x*(x-a)*(-a+2*x-2*a*x+2*x^2))),y,x);
 342
 343 set(%e^-x,%e^-x*'integrate((2*x^2+(2-2*a)*x-a)*%e^x/(sqrt(x)*sqrt(x-a)),x))$
 344
 345 odelin(('diff(y,x,2) = ((-a^2+(-1+a+a*(1+2*a))*x+(-1-a+(-1-a)*a)*x^2)*y
 346                     +((2*a-1)*x-4*a*x^2+(1+2*a)*x^3)*'diff(y,x,1))
 347                     /(x^2-2*x^3+x^4)),y,x);
 348 set((x-1)*x^a,(x-1)*x^a*log(x))$
 349
 350 odelin(2*y-2*x*'diff(y,x,1)+(x^2-1)*'diff(y,x,2),y,x);
 351 set((x-1)^2,x)$
 352
 353
 354 odelin(-y+4*x*'diff(y,x,1)+4*x^2*'diff(y,x,2),y,x);
 355 set(1/sqrt(x),sqrt(x))$
 356
 357 odelin(-15*y+2*'diff(y,x)+'diff(y,x,2),y,x);
 358 set(%e^-(5*x),%e^(3*x))$
 359
 360 odelin(y-(1+x)*'diff(y,x)+x*'diff(y,x,2),y,x);
 361 set(x+1,%e^x)$
 362
 363 odelin((x-1)*y+(1-2*x)*'diff(y,x)+x*'diff(y,x,2),y,x);
 364 set(%e^x,%e^x*log(x))$
 365
 366 odelin(n*y-2*x*'diff(y,x)+'diff(y,x,2),y,x);
 367 set(kummer_m((n+2)/4,1/2,-x^2)*%e^x^2*sqrt(abs(x))/sqrt(-x),
 368   kummer_u((n+2)/4,1/2,-x^2)*%e^x^2*sqrt(abs(x))/sqrt(-x))$
 369
 370 odelin(n*(1+n)*y-2*x*'diff(y,x)+(1-x^2)*'diff(y,x,2),y,x);
 371 set(gauss_a(-n,n+1,1,-((x-1)/2)),gauss_b(-n,n+1,1,-((x-1)/2)))$
 372
 373 odelin(n*y+(1-x)*'diff(y,x)+x*'diff(y,x,2),y,x);
 374 set(kummer_m(n+1,1,-x)*%e^x,kummer_u(n+1,1,-x)*%e^x)$
 375
 376 /* #3576 odelin wrong answer on simplest ode */
 377 odelin('diff(f,x)+f,f,x);
 378 set(exp(-x))$
 379
 380 odelin(x *'diff(f,x)+f,f,x);
 381 set(1/x)$
 382
 383 odelin(x *'diff(f,x)+f,f,x);
 384 set(1/x)$
 385
 386 odelin(x*'diff(f,x)-46*f,f,x);
 387 set(x^46)$
 388
 389 odelin('diff(f,x) + (46*x+107)*f,f,x);
 390 set(exp(-23*x^2-107*x))$
 391