Using reduction of order for Non-Homogenous DE

[juice34]

I need help solving a higher order differential equation by reduction of order.
It will be greatly appreciated if all steps are posted as well!

y(Double Prime)-3y(Prime)+2y=5e^3x where y sub one =e^x.

Ive tried to get the answer but end up with 3 constants.

 

[juice34]

the teachers example goes from w to u prime to u without integrating u prime to get u, where w=u prime and y=u*y(sub one)