If for x ≥ 0 , y = y x is the solution of the differential equation, x + 1 d y = x + 1 2 + y - 3 d x ,…

If for x≥0,y=yx is the solution of the differential equation, x+1dy=x+12+y-3dx,y2=0 then y3 is equal to ________

Solution

dydx=1+x+y-31+x

dydx-11+xy=1+x-3(1+x)

I.F=e-∫1(1+x)dx=1(1+x)

∴ddxy1+x=x+31+x-1+c

⇒y1+x=x+31+x-1+c

⇒y=1+xx+3(1+x)+c , ∴ at x=2, y=0

⇒0=32+1+c ⇒c=-3

At x=3, y=3

Asked in: JEE Main 2020 (09 Jan Shift 1)

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