JEE Math Practice 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.)
- A.$${C \over x}{e^{ - {1 \over x}}}$$
- B.$${C \over {{x^2}}}{e^{ - {1 \over x}}}$$
- C.$${C \over {{x^3}}}{e^{ - {1 \over x}}}$$
- D.$$C{x^3}\,{1 \over {{e^x}}}$$
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