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Old 2009-10-29, 01:39   #1
Joshua2
 
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Sep 2004

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Default solving 2nd order differential equations

so I have two part question.

I have a 2nd order linear homogeneous equation but the initial values aren't at y(0) and y'(0) like normal. They are @ -2 instead. So it seems there may be three ways to go about it. The first I thought of was to pretend it is at 0 and then try to shift the answer, but that is hard for complicated equations. I could also just plug everything in and solve two equations with two unknowns, but it is a lot of algebra. I think the teacher had a third way that might be the easiest similar to my 2nd way, but I couldn't understand it.

2nd question is solving inhomogeneous 2nd order linear
so our teacher has us solving these with an alpha beta method I don't really understand. But its solving to easier equations. let u=y'+ay and u' + Bu = the left hand side of the equation y'' + cy' + d. I couldn't find anyone on the net who used this method and explained. Everyone seems to use complicated stuff like Lagrange or Fourier or Wronskian

Last fiddled with by Joshua2 on 2009-10-29 at 01:58
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