The differential equation by eliminating the arbitary constants from the equation $y =$ $a cos x + b sin x + x sin x,$ where $y_{1} = \frac{d y}{d x}, y_{2} = \frac{d^{2} y}{d x^{2}}$ is

y_{2} + y = 3 cos x

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y_{2} + 2 y = 2 cos x

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y_{2} + y = 2 cos x

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y_{2} + y = 4 cos x

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Solution

The correct option is C $y_{2} + y = 2 cos x$
$y = a cos x + b sin x + x sin x$
$\Rightarrow y_{1} = - a sin x + b cos x + sin x + x cos x$
$\Rightarrow y_{2} = - a cos x - b sin x + cos x + cos x - x sin x$
$\Rightarrow y + y_{2} = 2 cos x$

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Similar questions

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y = a cos x + b sin x + x sin x

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Differential equation, having $y = (s i n^{- 1} x)^{2} + A (c o s^{- 1} x) + B$ where A and B are arbitary constants is $(p - x^{2}) \frac{d^{2} y}{d x^{2}} - \frac{x d y}{d x} = q$ ; then $p + q =$ ___

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The differential equation by eliminating the arbitary constants from the equation y= acosx+bsinx+xsinx, where y1=dydx,y2=d2ydx2 is

The correct option is C y2+y=2cosxy=acosx+bsinx+xsinx ⇒y1=−asinx+bcosx+sinx+xcosx ⇒y2=−acosx−bsinx+cosx+cosx−xsinx ⇒y+y2=2cosx

The differential equation by eliminating the arbitary constants from the equation $y =$ $a cos x + b sin x + x sin x,$ where $y_{1} = \frac{d y}{d x}, y_{2} = \frac{d^{2} y}{d x^{2}}$ is

The correct option is C $y_{2} + y = 2 cos x$
$y = a cos x + b sin x + x sin x$
$\Rightarrow y_{1} = - a sin x + b cos x + sin x + x cos x$
$\Rightarrow y_{2} = - a cos x - b sin x + cos x + cos x - x sin x$
$\Rightarrow y + y_{2} = 2 cos x$