$\frac{d y}{d x} = x^{2} + 2 x + 4$ find $y$ in terms of $x$

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Solution

$\frac{d y}{d x} = x^{2} + 2 x + 4 y = \int x^{2} + 2 x + 4 d x y = \int x^{2} d x + \int 2 x d x + \int 4 d x y = \frac{x^{3}}{3} + \frac{2 x^{2}}{2} + 4 x + c y = \frac{x^{3}}{3} + x^{2} + 4 x + c$

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