For x $ \in $ R, x $ \ne $ 0, if y(x) is a differentiable function such that x $\int\limits_1^x y $ (t) dt = (x + 1) $\int\limits_1^x ty $ (t) dt, then y (x) equals : (where C is a constant.)

Question

For x $ \in $ R, x $ \ne $ 0, if y(x) is a differentiable function such that

x $\int\limits_1^x y $ (t) dt = (x + 1) $\int\limits_1^x ty $ (t) dt, then y (x) equals :

(where C is a constant.)

${C \over x}{e^{ - {1 \over x}}}$

${C \over {{x^2}}}{e^{ - {1 \over x}}}$

${C \over {{x^3}}}{e^{ - {1 \over x}}}$

$C{x^3}\,{1 \over {{e^x}}}$

Solution

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