Question
Solve the differential equation $\frac{d y}{d x}=x^2 y+y$
$\begin{aligned} & \frac{d y}{d x}=x^2 y+y=\left(x^2+1\right) y \\ & \therefore \frac{1}{y} d y=\left(x^2+1\right) d x\end{aligned}$
Integrating on both sides, we get
$\begin{aligned} & \int \frac{1}{y} d y=\int\left(x^2+1\right) d x \\ & \therefore \log |y|=\frac{x^3}{3}+x+c\end{aligned}$
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