Question

(y + x²) dx + Caxt by? dye
E O​

Answer 1

You are wasting time by not putting parenthese () as needed. If you mean x*e^y - x^2 on the RHS, I cannot solve it. If you mean x * e^(y - x^2) then it is quite easy to solve, like so:

Multiply both sides by (e^(-y))dx to get (e^(-y)) * dy = (x * dx) * e^(-x^2).

The antiderivative of the LHS is -e^(-y).

For the RHS, let x^2 = u so that x * dx = du/2. Then the RHS becomes (e^(-u)) * du/2

and its anti-derivative is -(e^(-u)) /2 = -e^(-x^2) / 2.

So the solution is

-e^(-y) = -e^(-x^2) / 2 - C. (You can mutiply both sides by -1 if you wish.)