jee-main 2024 Q76

jee-main · India · session2_08apr_shift1 First order differential equations (integrating factor)

Let $y = y ( x )$ be the solution of the differential equation $\left( 1 + y ^ { 2 } \right) e ^ { \tan x } d x + \cos ^ { 2 } x \left( 1 + e ^ { 2 \tan x } \right) d y = 0 , y ( 0 ) = 1$. Then $y \left( \frac { \pi } { 4 } \right)$ is equal to
(1) $\frac { 2 } { e }$
(2) $\frac { 2 } { e ^ { 2 } }$
(3) $\frac { 1 } { e }$
(4) $\frac { 1 } { e ^ { 2 } }$

Let $y = y ( x )$ be the solution of the differential equation\\
$\left( 1 + y ^ { 2 } \right) e ^ { \tan x } d x + \cos ^ { 2 } x \left( 1 + e ^ { 2 \tan x } \right) d y = 0 , y ( 0 ) = 1$. Then $y \left( \frac { \pi } { 4 } \right)$ is equal to\\
(1) $\frac { 2 } { e }$\\
(2) $\frac { 2 } { e ^ { 2 } }$\\
(3) $\frac { 1 } { e }$\\
(4) $\frac { 1 } { e ^ { 2 } }$

Paper Questions

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