jee-main 2024 Q78

jee-main · India · session2_06apr_shift1 First order differential equations (integrating factor)

Let $y = y ( x )$ be the solution of the differential equation $\left( 2 x \log _ { e } x \right) \frac { d y } { d x } + 2 y = \frac { 3 } { x } \log _ { e } x , x > 0$ and $y \left( e ^ { - 1 } \right) = 0$. Then, $y ( e )$ is equal to
(1) $- \frac { 3 } { \mathrm { e } }$
(2) $- \frac { 3 } { 2 e }$
(3) $- \frac { 2 } { 3 e }$
(4) $- \frac { 2 } { \mathrm { e } }$

Let $y = y ( x )$ be the solution of the differential equation $\left( 2 x \log _ { e } x \right) \frac { d y } { d x } + 2 y = \frac { 3 } { x } \log _ { e } x , x > 0$ and $y \left( e ^ { - 1 } \right) = 0$. Then, $y ( e )$ is equal to\\
(1) $- \frac { 3 } { \mathrm { e } }$\\
(2) $- \frac { 3 } { 2 e }$\\
(3) $- \frac { 2 } { 3 e }$\\
(4) $- \frac { 2 } { \mathrm { e } }$

Paper Questions

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