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2014-04-25T14:55:27+05:30
(x^2)(d^2y/dx^2) + x(dy/dx) = 0 

Using the reduction order 

let dy/dx = w and d^2y/dx^2 = w' 

x^2w' + xw =0 w' + w/x = 0 

P(x) = 1/x Q(x) = 0 

IF = e^[∫dx/x] = e^[ln(x)] = x 

wx =∫ x(0)dx wx = C₁ w = C₁/x 

y' = w = y = ∫ w = ∫ C₁/xdx 

y = C₁ln(x) + C₂ 

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2014-04-25T15:00:55+05:30
The solution is in form of
y=klog_{e} (x)
substitute it in  the equation 
 x^{2}  \frac{d^2y}{dx^2}+x \frac{dy}{dx}= x^{2}  \frac{-k}{x^2}+x \frac{k}{x}=-k+k=0
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