We #160;have,dydx+4x=ex #8658;dydx=ex 4x #8658;dy=ex 4xdxIntegrating #160;both #160;sides, #160;we #160;get #8747;dy= #8747;ex 4xdx #8658;y= ...

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Relation between AM,GM,HM for 2 Numbers

dydx+4 x=e x

Question

$\frac{d y}{d x} + 4 x = e^{x}$

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Solution

$We have, \frac{d y}{d x} + 4 x = e^{x} \Rightarrow \frac{d y}{d x} = e^{x} - 4 x \Rightarrow d y = (e^{x} - 4 x) d x Integrating both sides, we get \int d y = \int (e^{x} - 4 x) d x \Rightarrow y = e^{x} - 2 x^{2} + C \Rightarrow y + 2 x^{2} = e^{x} + C$

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