Given the 2nd-order ODE
d^2 d
2------ f(x) - 4---- f(x) + 20f(x) = 2x
dx^2 dx
with initial conditions: f '(0)=2 and f(0)= 2
Determine the solution f(x)
This is an example of why some questions go unanswered.
The horrible text formatting just makes the eyes bleed.
Just use f' and f" for derivatives. It makes things much easier to read.
If you mean y" - 4y' + 20y = 2x
Then
Use the normal linear ODE methods to get
y = c1*e^(2x) sin4x + c2*e^(2x) cos4x + x/10 + 1/50