Solving y⁴ - 4y″ = 16e^(2x) with substitution

[lizlemon1991]

I'm working on this equation and I think I remember how to do it, but my notes from this class are so scattered and I can't seem to find the section in my textbook.

the problem is:

y⁽⁴⁾-4y" = 16e^2x

can someone help me out with just getting started? Doesn't it have something to do with letting w=y" and w"=y⁴?

 

[matematikawan]

You need to get the homogeneous solution and the particular solution.
To obtain the homogeneous solution use the characteristic equation.