jee-main 2022 Q89

jee-main · India · session1_27jun_shift2 First order differential equations (integrating factor)

Let $y = y ( x )$ be the solution of the differential equation $\left( 1 - x ^ { 2 } \right) d y = \left( x y + \left( x ^ { 3 } + 2 \right) \sqrt { 1 - x ^ { 2 } } \right) d x , - 1 < x < 1$ and $y ( 0 ) = 0$. If $\int _ { - \frac { 1 } { 2 } } ^ { \frac { 1 } { 2 } } \sqrt { 1 - x ^ { 2 } } y ( x ) d x = k$ then $k ^ { - 1 }$ is equal to

Let $y = y ( x )$ be the solution of the differential equation $\left( 1 - x ^ { 2 } \right) d y = \left( x y + \left( x ^ { 3 } + 2 \right) \sqrt { 1 - x ^ { 2 } } \right) d x , - 1 < x < 1$ and $y ( 0 ) = 0$. If $\int _ { - \frac { 1 } { 2 } } ^ { \frac { 1 } { 2 } } \sqrt { 1 - x ^ { 2 } } y ( x ) d x = k$ then $k ^ { - 1 }$ is equal to

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