I'm using Scientfic Notebook (a computer algebra system) to obtain the solution. (It's pretty ugly on paper.)

Here is the solution that Scientific Notebook gives us.

`i(t) =` ` -2.244 xx 10^{-4}\sin 19. 37t\cos 21.87t ` ` +\ 5.132 xx 10^{-5}\sin 19.37t\sin 21.87t` `+\ 2.815 xx 10^{-4}\sin 19.37t\cos 16.87t` ` -\ 8.345 xx 10^{-5}\sin 19.37t\sin 16.87t` ` -\ 8. 345 xx 10^{-5}\cos 19.37t\cos 16. 87t` ` -\ 2.815 xx 10^{-4}\cos 19. 37t\sin 16.87t` ` +\ 5.132 xx 10^{-5}\cos 19.37t\cos 21.87t` ` +\ 2.244 xx 10^{-4}\cos 19.37t\sin 21.87t` ` +\ 5.107 xx 10^{-3}e^{-5.0t} \sin 19.36t` ` +\ 3. 212 xx 10^{-5} e^{-5.0t}\cos 19.36t`

I hope you can see why I choose to use a computer algebra system to solve this kind of problem!

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