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Question

Solve the differential equation: yxdydx=x+ydydx

A
kx=ey/x
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B
kx=ey/x
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C
ky=ex/y
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D
ky=ex/y
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Solution

The correct option is A kx=ey/x
yxdydx=x+ydydx
Substitute y=vxdydx=v+xdvdx
x(xdvdx+v)+xv=x+x(xdvdx+v)v
dvdx=v21x(v+1)v+1v21dvdx=1x
Integrating both sides w.r.t x we get
v+1v21dvdxdx=1xdx
tan1v12log(v2+1)=logx+ckx=eyx

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