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Variable Separable Method

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Question

Solve : $\frac{d y}{d x} = \frac{3 e^{2 x} + 3 e^{4 x}}{e^{x} + e^{- x}}$

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Solution

Given:
$\frac{d x}{d y} = \frac{3 e^{2 x} - 3 e^{4 x}}{e^{x} - e^{- x}}$

solving the above integration by parts, we get

$y = 3 e^{3 x} - (3 e^{3 x} x - 3 e^{3 x}) + C$

$y = e^{3 x} + C$ (answer)

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