1(load("contrib_ode"),0); 20$ 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); */ 9sym:ode1_a(phi:(sin(x*y)+x*y*(cos(x*y)))/(x^2*cos(x*y)),y,x); 10[x,-y]; 11symtest(phi,sym[1],sym[2],y,x); 120; 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); */ 18sym:ode1_a(phi:(y/x)^2+2*(y/x), y, x); /* %psi_yyy=0 in ode1_a */ 19[x^2,-x^2]; 20symtest(phi,xi:sym[1],eta:sym[2],y,x); 210; 22mu:lie_integrating_factor(phi,xi,eta); 231/(-y^2-2*x*y-x^2); 24lie_exact(phi,mu,y,x); 25-y/(x*y+x^2) = %c; 26/* and the whole process */ 27ans:ode1_lie(phi,y,x); 28-y/(x*y+x^2) = %c; 29ode_check('diff(y,x)=phi,first(solve(ans,y))); 300; 31