jee-main 2016 Q84

jee-main · India · 10apr Differential equations Integral Equations Reducible to DEs

For $x \in R , x \neq 0$, if $y ( x )$ is a differentiable function such that $x \int _ { 1 } ^ { x } y ( t ) d t = ( x + 1 ) \int _ { 1 } ^ { x } t y ( t ) d t$, then $y ( x )$ equals (where $C$ is a constant)
(1) $C x ^ { 3 } e ^ { \frac { 1 } { x } }$
(2) $\frac { C } { x ^ { 2 } } e ^ { - \frac { 1 } { x } }$
(3) $\frac { C } { x } e ^ { - \frac { 1 } { x } }$
(4) $\frac { C } { x ^ { 3 } } e ^ { - \frac { 1 } { x } }$

For $x \in R , x \neq 0$, if $y ( x )$ is a differentiable function such that $x \int _ { 1 } ^ { x } y ( t ) d t = ( x + 1 ) \int _ { 1 } ^ { x } t y ( t ) d t$, then $y ( x )$ equals (where $C$ is a constant)\\
(1) $C x ^ { 3 } e ^ { \frac { 1 } { x } }$\\
(2) $\frac { C } { x ^ { 2 } } e ^ { - \frac { 1 } { x } }$\\
(3) $\frac { C } { x } e ^ { - \frac { 1 } { x } }$\\
(4) $\frac { C } { x ^ { 3 } } e ^ { - \frac { 1 } { x } }$

Paper Questions

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