Question

Given the differential Equation y'+2y=2e^x ;solve this equation using the integration factor; solve for y to get the general solution.

Answer 1

$y'+2y=2e^x\Longrightarrow y'=2e^x-2y$

If $f'(x)=g(x)$ then $y=\int{g(x)dx}$

So we extract,

$y=\int{2e^x-2x}dx$

Which becomes,

$y=2e^x-x^2+C$

Hope this helps.

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