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[ x tan(y/x) - y sec^2(y/x) ] dx + x sec...

`[ x tan(y/x) - y sec^2(y/x) ] dx + x sec^2 (y/x)] dy= 0`

Text Solution

Verified by Experts

Let `y = vx`
Then, `dy/dx = v+x(dv)/dx`
Our given equation becomes,
`[xtanv-vxsec^2 v]dx + xsec^2v dy = 0`
`=>-dy/dx = [xtanv-vxsec^2 v]/[xsec^2v]`
`=>-v-x(dv)/dx = tanv/(sec^2v) - v`
`=>- dx/x = (sec^2v dv)/tanv`
Now, integrating both sides,
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