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## Homework Statement

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'' - k

^{2}y = R

_{(x)}, with k ≠ 0 a real constant, show that it has a particular solution:

y1 = (1/k)∫R sinh[k(-t)] dt

## Homework Equations

## 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?

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