10 ! full answer in step by step

After a little manipulation, the given diff'l equation will look like this:

e^y * dy = (2x + 1) * dx.
                                                             x^2
Integrating both sides, we get e^y = 2 + x + c, or e^y = x^2 + x + c
                                                               2

Now let x=0 and y = 1, o find c:

e^1 = 0^2 + 0 + c.  So, c = e, and the solution is e^y = x^2 + x + e.