Simplify differential equation

[parisse]

lrdheat, the solution you give does not work unless I make a mistake
c:=-2*exp(t^2)/((t^2-1)*(exp(t^2)-2*c1));
simplify(diff(c,t)-(t^3*c^2+2*t*c)) does not return 0.
(t^2-1) should not be in factor.
Solving by hand, set z=1/y, z'=-y'/y^2=-(t^3*y^2+2*t*y)/y^2=-t^3-2*t*z is linear in z. General solution w/o second member z=K*exp(-t^2), z=(1-t^2)/2 is a particular solution, general solution in z=(1-t^2)/2+K*exp(-t^2), then y=1/z. Xcas/Prime solution is indeed correct