If y(x) is the solution of the differential equation x ,dy - (y^2 - 4y) ,dx = 0 for x > 0, y(1) = 2, and the slope of the curve y = y(x) is never zero, then the value of 10 ,y( 2 ) is _____.

JEE Advanced 2022 Mathematics question

If is the solution of the differential equation

x dy - - 4y) dx = 0 for x > 0, y(1) = 2,

and the slope of the curve is never zero, then the value of is .

Answer: 8

Separating variables: . At , : , so \dfrac{y-4}{y}$| =

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Question ID VK-034009