# Solve the differential equation (\sin 2x)y'=e^{5y}\cos 2x

## Question:

Solve the differential equation {eq}(\sin 2x)y'=e^{5y}\cos 2x {/eq}

## Differential equation:

The differential equation {eq}y'=f(x) {/eq} is called separable differential equation.

To solve this problem we'll integrate both sides and use the common integral {eq}\displaystyle \int \cot x \ dx = \ln|\sin x| {/eq}

We are given:

{eq}\displaystyle (\sin 2x)y'=e^{5y}\cos 2x {/eq}

This is a first order separable ordinary differential equation.

So rewrite in the...

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