can anyone help with solving this?

jacob s2020-09-03T15:45:54Z

Can anyone help with solving this please? y" - 4y' +4y=e^2x+2. 

p(x) = e2x + 2

Therefore yp has the form Ae2x + B:

yp ' =2Ae2x

4yp' + 4yp = 8Ae2x + 4Ae2x + 4B = 12Ae2x + 4B = e2x + 2

12A = 1 -> A = 1/12

4B = 2 -> B = 1/2

Therefore:

yp = (1/12)e2x + 1/2