Question
Solve the following differential equations:
$\frac{d y}{d x}=x^2 y+y$
$\frac{d y}{d x}=x^2 y+y$
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$\frac{d^2 y}{d x^2}+5 \frac{d y}{d x}+y=x^3$
$\sin ^{-1}\left(\sqrt{\frac{1+x^2}{2}}\right)$
$\int_0^4\left[\sqrt{x^2+2 x+3}\right]^{-1} d x$