share/contrib/diffequations/tests/rtestode_murphy_2_3.mac

   1 (load("contrib_ode"),0);
   2 0$
   3
   4 /* ODE tests - Murphy equations 2.201 - 2.300
   5
   6   Reference:
   7     G M Murphy, Ordinary Differential Equations and Their
   8     Solutions, Van Nostrand, 1960, pp 15-23
   9
  10     First Order and Second or Higher Degree, p278 ff
  11 */
  12
  13 /* Don't kill(all); It messes up trigsimp */
  14
  15 /* Eliminate parameter t from singular solution */
  16 (elim_(ans,x,y,t):=block([s],s:first(solve(ans[2],t)),s:solve(ev(ans[1],s),y),s[1]),done);
  17 done;
  18
  19 /* Print ode number*/
  20 (pn_(n_):=print("Murphy ODE 2.",n_),true);
  21 true;
  22
  23 /* 252 */
  24 /*(pn_(252),ans:contrib_ode(eqn:a^2*(b^2-(c*x-a*y)^2)*'diff(y,x)^2+2*a*b^2*c*'diff(y,x)+c^2*(b^2-(c*x-a*y)^2)=0,y,x));*/
  25
  26 /* 285 */
  27 (pn_(285),ans:contrib_ode(eqn:'diff(y,x)^3+a*x*'diff(y,x)-a*y=0,y,x));
  28 [y=(%c*a*x+%c^3)/a,y=-2*x*sqrt(-a*x)/(3*sqrt(3)),y=2*x*sqrt(-a*x)/(3*sqrt(3))];
  29 [method,ode_check(eqn,ans[1]),ode_check(eqn,ans[2]),ode_check(eqn,ans[3])];
  30 [clairaut,0,0,0];
  31
  32 /* 286 */
  33 (pn_(286),ans:contrib_ode(eqn:'diff(y,x)^3-(a+b*x)*'diff(y,x)+b*y=0,y,x));
  34 [y=(%c*b*x+%c*a-%c^3)/b,y=-2*(b*x+a)^(3/2)/(3*sqrt(3)*b),y=2*(b*x+a)^(3/2)/(3*sqrt(3)*b)];
  35 [method,ode_check(eqn,ans[1]),ode_check(eqn,ans[2]),ode_check(eqn,ans[3])];
  36 [clairaut,0,0,0];
  37
  38 /* 297 */
  39 (pn_(297),ans:contrib_ode(eqn:'diff(y,x)^3-'diff(y,x)^2+x*'diff(y,x)-y=0,y,x));
  40 [y=%c*x+%c^3-%c^2,y=-((sqrt(1-3*x)*(6*x-2)-9*x+2)/27),y=(sqrt(1-3*x)*(6*x-2)+9*x-2)/27];
  41 [method,ode_check(eqn,ans[1]),ode_check(eqn,ans[2]),ode_check(eqn,ans[3])];
  42 [clairaut,0,0,0];