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## Homework Statement

Solve

[tex]y''(t) - k^2 y(t) = e^{-a|t|}[/tex] where a and k are both positive and real.

## Homework Equations

The solution was obtained trough a fourier transform.

## The Attempt at a Solution

I got the solution

[tex]y(t) = \frac{ke^{-at} - ae^{-kt}}{k(a^2 - k^2)}[/tex]

but when i plug it back into the differential equation i just get

[tex]e^{-at}[/tex]

how could I get the absolute value back in there?

Might there be anything wrong with my solution procedure?