Question

how do you find the general solution of xy'=y+x^2e^x

Answer 1

\[xy'=y+x^2e^x\]\[\frac{xy'-y}{x^2}=e^x\]\[\left(\frac{y}{x}\right)'=e^x\]\[\frac{y}{x}=e^x+C\]\[y=x(e^x+C)\]