share/contrib/diffequations/tests/rtest_ode_sym2.mac

   1 (load("contrib_ode"),0);
   2 0$
   3
   4 /* Test cases for ode1_lie functions */
   5
   6 /* Some exact equations from rtestode */
   7
   8 /* ode2(x^2*cos(x*y)*'diff(y,x) + (sin(x*y)+x*y*(cos(x*y)))=0, y, x); */
   9 sym:ode1_a(phi:(sin(x*y)+x*y*(cos(x*y)))/(x^2*cos(x*y)),y,x);
  10 [x,-y];
  11 symtest(phi,sym[1],sym[2],y,x);
  12 0;
  13
  14 /* ode2( (2*x*y-exp(-2*y))*'diff(y,x)+y=0, y, x); */
  15 /* sym:ode1_a(phi:-y/(2*x*y-exp(-2*y)),y,x); BAD */
  16
  17 /* ode2( 'diff(y,x)=(y/x)^2+2*(y/x), y, x); */
  18 sym:ode1_a(phi:(y/x)^2+2*(y/x), y, x); /* %psi_yyy=0 in ode1_a */
  19 [x^2,-x^2];
  20 symtest(phi,xi:sym[1],eta:sym[2],y,x);
  21 0;
  22 mu:lie_integrating_factor(phi,xi,eta);
  23 1/(-y^2-2*x*y-x^2);
  24 lie_exact(phi,mu,y,x);
  25 -y/(x*y+x^2) = %c;
  26 /* and the whole process */
  27 ans:ode1_lie(phi,y,x);
  28 -y/(x*y+x^2) = %c;
  29 ode_check('diff(y,x)=phi,first(solve(ans,y)));
  30 0;