The solution of the differential equation x4+y4dx−xy3dy=0 is

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cx=ey/x4

cy=ey/x4

cy=ex/y3

cx=ex3y

answer is A.

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Detailed Solution

The given equation can be written as⇒dydx=x4+y4xy3=xy3+yx put y=vx then dydx=v+xdvdx⇒v+xdvdx=1v3+v⇒∫v3dv=∫dxx⇒v44=log⁡x+log⁡c=log⁡cx⇒cx=e1v4=e yx4

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