Find the general solution to the differential equation y'' -16y = 0, where y is a function of x. Give initial conditions that would give a unique solution to the eqution.
For the differential equation y'' - k2y = R(x), with k ≠ 0 a real constant, show that it has a particular solution:
y1 = (1/k)∫R sinh[k(-t)] dt
The Attempt at a Solution
No problems with part (a) and finding homogeneous solution.
I tried to avoid expanding the integral using integration by parts by differentiating both LHS and RHS w.r.t. x. But I'm missing a dR/dx term...
Is there anything wrong with my integration for part (c) below?