Verify that the differential equation:

has as its solution:

where A and B are arbitrary constants. Show also that this solution can be written in the form:

And express C and as functions of A and B.

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- Dec 4th 2008, 08:49 AMArythDifferential Equations
Verify that the differential equation:

has as its solution:

where A and B are arbitrary constants. Show also that this solution can be written in the form:

And express C and as functions of A and B. - Dec 4th 2008, 09:26 AMChris L T521
The differential equation is equivalent to . The corresponding auxiliary equation is . This implies that the corresponding solutions are and

Thus, the general solution has the form

However, by Euler's formula, we see that and

Thus,

Letting and , we see that the general solution is

Now,

I don't see how the last step is . I believe it should only be . I may be wrong, though. Anyone can correct me if needed...

Does this make sense? - Dec 4th 2008, 09:49 AMAryth
You're right... There is no C before the Re.

One thing though, there should be an i before the arctan in your final solution.

Thanks though, I understand it now. - Dec 4th 2008, 10:48 AMChris L T521