Prove that if $y = \frac{sin x}{x}$ $y= sinx/x$ , show that $\frac{d^{2} y}{{d x}^{2}} + \frac{2}{x} \frac{d y}{d x} + y = 0$ $(d^2y)/(dx^2) + 2/x dy/dx + y = 0$ ?

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Answer 1 · 2018-05-13T20:33:21

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If $x y = sin x$ $xy = sin x$ , using the product rule:

$triangle/ x + square implies$

$(2y')/x + y'' + color( red)( y + xy') = - color(blue)((sin x)/x) + cos x$

As $color(blue)(y = (sin x)/x)$ and $color(red)( y + xy' = cos x)$ :

Prove that if y= sinx/xy=sinxxy= sinx/x, show that (d^2y)/(dx^2) + 2/x dy/dx + y = 0d2ydx2+2xdydx+y=0(d^2y)/(dx^2) + 2/x dy/dx + y = 0 ?