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Question

The family of curves which satisfies the differential equation y exydx=(x exy+y2)dy, (y0) is
(where C is the constant of integration )

A
y exy=C
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B
y+exy=C
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C
xeyx=C
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D
yexy=C
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Solution

The correct option is D yexy=C
y exydx=(x exy+y2)dy, (y0)
dxdy=x exy+y2y exy
Put x=vy
dxdy=v+ydvdy
v+ydvdy=v+yev
ev dv=dy
ev+C=y
yexy=C

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