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Q.

The solution of the differential equation xy1 = 2x ey/x + y is

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a

ey/x+In cx

b

ey/x+In cx=0

c

e-y/x=x+c

d

e-y/x=2lx+cx

answer is D.

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Detailed Solution

xy=2xe-y/x+y

Put  yx=V  y=Vx  y=V+xdvdx

  xV+xdvdx=2x e-y/x+y  V+xdvdx=2e-y/x+yx  V+x dvdx=2e-y/x+V  2e-y/x=xdvdx  2eV=xdvdx  1e-Vdv=2dxx  eV dv=2x dx  eV=2log |x|+C  ey/x=2log Cx

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The solution of the differential equation xy1 = 2x e–y/x + y is