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Variable Separable Method

The solution ...

Question

The solution of $(1 + e^{x}) y d y = e^{x} d x$ is:

y^{2} = log c (e^{x} + 1)

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\frac{y^{2}}{2} = log c e^{x}

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\frac{y^{2}}{2} = log c (e^{x} + 1)

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2 y = log c (e^{x} + 1)

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Solution

The correct option is D $\frac{y^{2}}{2} = log c (e^{x} + 1)$
$(1 + e^{x}) y d y = e^{x} d x$

$\int y d y = \int (\frac{e^{x}}{1 + e^{x}}) d x + c$

$\Rightarrow \frac{y^{2}}{2} = log (1 + e^{x}) c$

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