Allright, my question is simple (problem isn't though) - can anyone give me in good detail how to solve this equation:
(1 + X)*(d^2y/dx^2) +x*(dy/dx) -y = 0; y1=x
The idea is that, there is a solution of this equation already (y=x), but I am looking for a second solution. And the technique I am supposed to use, is to substitude in a "v" in front of the function, ie, "y2=xv", then "dy2/dx=xdv +v" and "dy2^2/dx^2=xd^2v + 2dv". Then you substitue this information in for the original equation, factor out DV and D^2V, then create another substitution for w=dV and dw=d^2v. Finally, you can set w and x on seperate sides, integrate, solve for w, then solve backwards back to v, and finally come up with the second solution y2 from the equation y=xv.
I've worked the problem, and I know how to solve these problems, it just seems I keep making the same mistakes and can't solve it. If anyone could actually go through the entire process and tell me how they did it, it would be greatly appreciated.
2007-04-26
16:30:17
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2 answers
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asked by
Xan
3
in
Mathematics