if y=cos(logx) +3sin(logx) prove that x^2 (d^2 x/dx^2 )+x(dy/dx)+y=0


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Question Number 43489 by peter frank last updated on 11/Sep/18

$i f y = c o s (l o g x) + 3 s i n (l o g x) p r o v e t h a t$ $x^{2} \frac{d^{2} x}{{d x}^{2}} + x \frac{d y}{d x} + y = 0$
	Answered by tanmay.chaudhury50@gmail.com last updated on 11/Sep/18

	$\frac{d y}{d x} = - s i n (l o g x) \times \frac{1}{x} + 3 c o s (l o g x) \times \frac{1}{x}$ $x \frac{d y}{d x} = - s i n (l o g x) + 3 c o s (l o g x) =$ $x \frac{d^{2} y}{{d x}^{2}} + \frac{d y}{d x} = - c o s (l o g x) \times \frac{1}{x} - 3 s i n (l o g x) \times \frac{1}{x}$ $x^{2} \frac{d^{2} y}{{d x}^{2}} + x \frac{d y}{d x} = - y$ $x^{2} \frac{d^{2} y}{{d x}^{2}} + x \frac{d y}{d x} + y = 0$
	Commented by peter frank last updated on 11/Sep/18

	$m u c h r e s p e c t s i r$
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