jee-main 2023 Q75

jee-main · India · session2_15apr_shift1 First order differential equations (integrating factor)

Let $x = x ( y )$ be the solution of the differential equation $2 ( y + 2 ) \log _ { e } ( y + 2 ) d x + \left( x + 4 - 2 \log _ { e } ( y + 2 ) \right) d y = 0 , y > - 1$ with $x \left( e ^ { 4 } - 2 \right) = 1$. Then $x \left( e ^ { 9 } - 2 \right)$ is equal to
(1) 3
(2) $\frac { 4 } { 9 }$
(3) $\frac { 32 } { 9 }$
(4) $\frac { 10 } { 3 }$

Let $x = x ( y )$ be the solution of the differential equation $2 ( y + 2 ) \log _ { e } ( y + 2 ) d x + \left( x + 4 - 2 \log _ { e } ( y + 2 ) \right) d y = 0 , y > - 1$ with $x \left( e ^ { 4 } - 2 \right) = 1$. Then $x \left( e ^ { 9 } - 2 \right)$ is equal to\\
(1) 3\\
(2) $\frac { 4 } { 9 }$\\
(3) $\frac { 32 } { 9 }$\\
(4) $\frac { 10 } { 3 }$

Paper Questions

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