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.
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.
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?