Find y(x) for y''(x)-g'(x)y'(x)/g(x)+g(x)^2*y(x)=0

steventkl

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Sep 28, 2007
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For any function g(x), and given equation, y''(x) - g'(x)y'(x)/g(x) + g(x)^2*y(x) = 0, to find y(x) in terms of some integratino of g(x)

I have faced the g(x) as its coefficient at the first time, and I have seen a lot with constant coefficient, but not this one.

By the solve of a(x)y'' + b(x)y' + c(x)y = f(x), assume yc = c1y1 + c2y2

For y_p = v1(x)y1 + v2(x)y2, where v1(x) and v2(x) are the variable parameters.
From the prove, finally we found

v1 = - Int( [y2f(x) / a(x) W[y1,y2]] dx)
v2 = Int( [y1f(x) / a(x) W[y1,y2]] dx)

where Int = Integration

what should i do after this step? just according to f(x) = 0 and put it equal to 0??
plz help~~thx~
 
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