Fourier transform of differentials equation

[naspek]

I just noticed that you have an error in your expression. Convolution tells you that $y(x)=\frac{1}{2a}\int_{-\infty}^{\infty}f(x-t)e^{-a|t|}dt$, not $\frac{1}{2a}\int_{-\infty}^{\infty}f(x-t)e^{-a|x|}dt$.

change it already.. thanks

 

[naspek]

the first part of the general solution should be c1(cos XXXX) + c1(sin XXXX) right?
just ignore the XXXX.. just want to know the pattern..