jee-advanced 2022 Q2

jee-advanced · India · paper2 3 marks Differential equations Solving Separable DEs with Initial Conditions
If $y ( x )$ is the solution of the differential equation
$$x d y - \left( y ^ { 2 } - 4 y \right) d x = 0 \text { for } x > 0 , \quad y ( 1 ) = 2$$
and the slope of the curve $y = y ( x )$ is never zero, then the value of $10 y ( \sqrt { 2 } )$ is $\_\_\_\_$ .
If $y ( x )$ is the solution of the differential equation

$$x d y - \left( y ^ { 2 } - 4 y \right) d x = 0 \text { for } x > 0 , \quad y ( 1 ) = 2$$

and the slope of the curve $y = y ( x )$ is never zero, then the value of $10 y ( \sqrt { 2 } )$ is $\_\_\_\_$ .