But how can i learn complex functions and differentials? What kind of books?

I'm eager to learn it, could you recommand me a book on this kinda stuff? thanks ]]>

If you want to try solving your question with complex methods, use the fact that

If you have, for example, sin(7t), you simply put a 7 in the exponent of e^(ix).

Your question is the most simple example, cos(t), so I think you can follow it quite easily.

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We know that

from above. Let and , so we get:,And so

Which means that

Thus, we must have that

since all derivatives disappear, which givesSo

Which becomes

Since

, this must mean thatI hope I didn't miss anything out.

]]>But numen, I've never heard of solving using complex functions.

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For cosx and sinx I prefer using complex e-functions. Like cosx = Re[e^(ix)]. Try that method, it's really good imho, also if you have cos(7x) or similiar it works great.

I can give you a full solution to it later if you want, I got math exams tomorrow

Have you learned methods of solving 2nd order DEs? I would go with Variation of Parameters for this one. Let me know if you haven't, I can show you how to do it.

]]>So anyone know how to answer my original question?

]]>The next question goes: y''+y'+2y=t^2+e^-t+cos t.

Do I just find y''+y'+2y'=cos t? I've already calculated for t^2 and e^-t as was shown by numen. Then after I get all these, I just add them together with A and B. Is it right?

]]>Let (z is a function, z(t))

So we get

So

Let z=Ct+D, so z'=C and z''=0; then C must be 1, which gives z=t.

Whohoo, first time using these codes

]]>y''+3y'+2y=e^(-t)

Thanks for helping.

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