Differential Equation
WARNING HOMEWORK PROBLEM:
I have stumbled across a very strange integration problem.
I'm trying to find all of the solutions to the equation
y"+9y=sin(3x)
That's all fine, well, and good, except part of the problem requires me to integrate the equation
u1'(x) = -i/6*e^(-3ix)sin(3x)
and another of the same basic form
I'm positive that the integral of e^(ax)sin(bx) = e^(ax)/(a^2+b^2)*(a*sin(bx)-b*cos(bx)), but in this case a^2+b^2 = 0, leaving the integral undefined...any ideas??
Since you could have done this yourself: The wolfram integrator has the answer, but not the intermediate steps.
Sorry, I forgot to mention that I used maple to find an answer. I'm just trying to figure out how to arrive at an answer. It seems that I need to take a closer look at the specific integration that creates this problem, however, the only method I see to solve it is using integration by parts to obtain an algebraic equation that I can solve for the integral, which is what led me to the a^2 + b^2 denominator in the first place.
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