Simplify differential equation

[parisse]

[a]:=desolve(diff(y,t)=t^3*y^2+2t*y,t,y);
then lin(a) returns (-1/2*(t^2-1)+c_0*exp(-t^2))^-1
I don't think it's the same as your book.
simplify(diff(a,t)-(t^3*a^2+2t*a) returns 0, but
b:=1/(c*e^(t^2)-(2+t^2))
simplify(diff(b,t)-(t^3*b^2+2t*b))
does not return 0.
Perhaps you made a mistake in entering the equation, or the book solution is wrong.