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Show that the differential equation x...

Show that the differential equation `xcos(y/x)(dy)/(dx)=ycos(y/x)+x` is homogeneous and solve it.

Text Solution

Verified by Experts

Let `y/x = v`
Then, `y = vx =>dy/dx = v+x(dv)/dx`
So, given equation becomes,
`xcosv(dy/dx) = vxcosv+x`
`=>dy/dx = (vxcosv+x)/(xcosv)`
`=> v+x(dv)/dx = (vcosv+1)/(cosv)`
`=> v+x(dv)/dx = v+secv`
`=>x(dv)/dx = secv`
...
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