Let the solution curve of the differential equation x d y-y d x= x^ 2 +y^ 2 d x, x0, y(1)=0, be y=y(x). Then y(3) is equal to

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Let the solution curve of the differential equation x d y-y d x= x^ 2 +y^ 2 d x, x>0, y(1)=0, be y=y(x). Then y(3) is equal to

Quantrex Academy · Accepted Answer

Correct answer: B. 4

xdy - ydx = x^2+y^2 \,dx. Put y = vx: x^2 dv = x 1+v^2 \,dx. dv 1+v^2 = dx x . Integrating: (v+ 1+v^2 ) = x + C. y(1) = 0 v = 0 at x = 1: C = 0. v + 1+v^2 = x y + x^2+y^2 = x^2. At x = 3: y + 9+y^2 = 9 9+y^2 = (9-y)^2 18y = 72 y = 4.

JEE Main Mathematics Question (2026) — Solution

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