jee-advanced 2023 Q9

jee-advanced · India · paper2 4 marks First order differential equations (integrating factor)
For $x \in \mathbb { R }$, let $y ( x )$ be a solution of the differential equation $$\left( x ^ { 2 } - 5 \right) \frac { d y } { d x } - 2 x y = - 2 x \left( x ^ { 2 } - 5 \right) ^ { 2 }$$ such that $y ( 2 ) = 7$. Then the maximum value of the function $y ( x )$ is
For $x \in \mathbb { R }$, let $y ( x )$ be a solution of the differential equation
$$\left( x ^ { 2 } - 5 \right) \frac { d y } { d x } - 2 x y = - 2 x \left( x ^ { 2 } - 5 \right) ^ { 2 }$$
such that $y ( 2 ) = 7$. Then the maximum value of the function $y ( x )$ is