Simplify :
$x y + (x y + 4 x^{3} + 3 x - 5) - (- 3 x^{2} - 4) - (x y + x^{3} - 4)$

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Solution

$x y + (x y + 4 x^{3} + 3 x - 5) - (- 3 x^{2} - 4) - (x y + x^{3} - 4)$ = $x y + x y + 4 x^{3} + 3 x - 5 + 3 x^{2} + 4 - x y - x^{3} + 4$
$= x y + 3 x^{3} + 3 x + 3 + 3 x^{2}$

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The solution of the differential equation $x \frac{d y}{d x} + y = x^{2} + 3 x + 2$ is

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x = 6

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