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My function:

d

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 might have 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.

d

^{2}f/dx^{2}+ 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 might have 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.