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.

r3t40