jee-main 2021 Q88

jee-main · India · session1_25feb_shift2 Differential equations Solving Separable DEs with Initial Conditions
If the curve $y = y ( x )$ represented by the solution of the differential equation $\left( 2 x y ^ { 2 } - y \right) d x + x \, d y = 0$, passes through the intersection of the lines $2 x - 3 y = 1$ and $3 x + 2 y = 8$, then $| y ( 1 ) |$ is equal to $\underline{\hspace{1cm}}$.
If the curve $y = y ( x )$ represented by the solution of the differential equation $\left( 2 x y ^ { 2 } - y \right) d x + x \, d y = 0$, passes through the intersection of the lines $2 x - 3 y = 1$ and $3 x + 2 y = 8$, then $| y ( 1 ) |$ is equal to $\underline{\hspace{1cm}}$.