The solution of the equation x2d2 y-d x2-In- x- when x-1- y-0 and d y-d x-1 is A- y-1-2ln x2-ln xB- y-1-2ln x2-ln xC- y -1-2ln x 2-ln xD- y-1-2ln x2-ln x

The correct option is D y= 1/2(ln x)^2 ln xd^2y/dx^2=logx/x^2⇒dy/dx= (logx+1)/x+c At dy/dx= 1, x=1, y =0, ∴ c =0 ⇒ y = ∫log x+1/xdx= 1/2(log x)^2 log x. ...

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Byju's Answer

Standard XII

Mathematics

Variable Separable Method

The solution ...

Question

The solution of the equation $x^{2} \frac{d^{2} y}{d x^{2}}$ =In ~x, when x=1, y =0 and $\frac{d y}{d x} = - 1$ is

y = \frac{1}{2} (l n x)^{2} + l n x

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y = \frac{1}{2} (l n x)^{2} - l n x

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y = - \frac{1}{2} (l n x)^{2} + l n x

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y = - \frac{1}{2} (l n x)^{2} - l n x

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Solution

The correct option is D $y = - \frac{1}{2} (l n x)^{2} - l n x$
$\frac{d^{2} y}{d x^{2}} = \frac{l o g x}{x^{2}} \Rightarrow \frac{d y}{d x} = \frac{- (l o g x + 1)}{x} + c$
At $\frac{d y}{d x} = - 1, x = 1, y = 0, ∴ c = 0$
$\Rightarrow y = - \int \frac{l o g x + 1}{x} d x = - \frac{1}{2} (l o g x)^{2} - l o g x$ .

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The solution of the equation x2d2ydx2 =In ~x, when x=1, y =0 and dydx=−1 is

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The solution of the equation $x^{2} \frac{d^{2} y}{d x^{2}}$ =In ~x, when x=1, y =0 and $\frac{d y}{d x} = - 1$ is