Solve and find the general solution of y

Question

(3x+1)y"-(12x+5y)y'+6y(2x+1)=28⁴√(3x+1)³.•e²x

Help me out please ......

Answer 1

You sure you didn't mean
(3x+1)y"-(12x+5)y'+6y(2x+1)=28*(3x+1)^(3/4)*e^(2x)
because e^2 * x is just very incongruous, and that 12x+5y makes it nonlinear.

Check out integrating factors.

Answer 2

I saw e^2 * x but I suspect it was a typo from them

But can you show me how to do it
Having e^(2x)

I will follow your step all through