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The solution of differential equation xy3(1+cos⁡x)−ydx+xdy=0 is

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a

y=x3+2xsinx+xcosx−2sinx+c

b

x33+2cosx−xsinx+c

c

x33+x2sinx−2xsinx+cosx+c

d

x22y2=x33+x2sinx+2xcosx−2sinx+c

answer is D.

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Detailed Solution

dydx+y3(1+cos⁡x)−yx=0−1y3dydx+1y2x=(1+cos⁡x) Put +1y2=u⇒−2y3dydx=dudx12dudx+1xu=1+cos⁡xdudx+2xu=2(1+cos⁡x) I. F=e2∫1xdx=x2 G.S is 1y2x2=∫2(1+cos⁡x)x2dxx22y2=∫x2dx+∫x2cos⁡xdxx22y2=x33+x2sinx+2xcosx-2sinx+c

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The solution of differential equation xy3(1+cos⁡x)−ydx+xdy=0 is