Trying to solve a second order differential with delta function

My function:

d²f/dx² + cf = delta(x)

Condition: f is finite and f(50) = f(-50) = 0

Solution: f = C₁exp(cx) + C₂exp(-cx)

Due to condition,

f = C₁exp(cx) for x<=0 and C₂exp(-cx) for x>=0

f(50) = C₂exp(-c*50) = 0 = > C₂ = 0

Likewise, for C₁

I don't know if I missed something. Also not sure if I dealt with the delta function correctly. I assumed RHS as zero for the purpose of solving the equation.

Edited October 12, 20187 yr by random_soldier1337