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If y = 3 cos(logx) + 4 sin(logx), show that x^2 d^2y/dx^2+x+dy/dx+y=0

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If y = 3 cos(logx) + 4 sin(logx), show that

x2 d2y/dx2+x+dy/dx+y=0

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Given, y = 3 cos (log x) + 4 sin (log x)
Differentiating w.r.t. x, we have

Again differentiating w.r.t. x, we have

calculating the value of y2

Now, L.H.S. = x2 y2 + xy1 + y

Evaluating L.H.S

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