calculus integration differentiation

[parisse]

Divide by dx, you have a differential equation, use desolve. Note that a desolve error can give some interesting information, like for the last one
"Unable to isolate y in exp(y)*x^2*y^3+x^2*y^2+x+y^3*c_1"
which means that the diff eq was solved but the solver was not able to express y in terms of x.