Answer
$y=Ae^{\frac{x^2}{2}}-2$
Work Step by Step
We are given that $ \dfrac{dy}{dx}=xy+2x$
We will separate the variables to obtain:
$\dfrac{dy}{dx}=x(y+2)$
Integrate to obtain:
$\int \dfrac{\ dy}{y+2}=\int x \ dx$
This implies that $\ln |y+2|=\dfrac{x^2}{2}+C$
or, $e^{\ln |y+2|}=e^{\frac{x^2}{2}}e^C$
Suppose that $A=e^C$
Therefore, we have: $y=Ae^{\frac{x^2}{2}}-2$
