e^x dy + (y e^x + 2x)dx = 0

We can write above equation as

Divide both sides by e^x we get,

Since it is a form of linear differential equation.

Integrating Factor (I.F) = e^{∫ p dx}

I.F = e^{∫ 1 dx} = e^x

Solution of differential equation is given by

y.(I.F) = ∫ Q.(I.F) dx + C

⇒ y e^x + x² = C = (C)