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# Solve the differential equation.$(e^y - 1)y' = 2 + \cos x$

## $c^{y}-y=2 x+\sin x+C$

#### Topics

Differential Equations

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### Video Transcript

this question asks us to solve the differential equation. Eat of the Y minus one times why one which we can write his D y over DX is equivalent to two plus co sign X. Now we know that we want the wise on one side and the exes on one side. So in other words, we need to bring DX over to this side. We bring it over to the right hand side by multiplying book sides by Deac Sweet cancels off from the left. As you can see I'm doing right now. Take the integral of both sides Integrate left hand side to be e the y minus y on the right hand side were adding a variable 2 to 2 acts, plus integral of Cosa nexus, sign axe and then plus C or constant of integration.

#### Topics

Differential Equations

Lectures

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