Kushagra Madhukar
Last Activity: 4 Years ago
Dear student,
Please find the solution to your question.
Given, xdy /dx= y (log y - log x + 1)
→ dy/dx = y/x (log(y/x) + 1)
Let, y = vx
Hence, dy/dx = v + x.dv/dx
→ v + x.dv/dx = v (logv + 1)
→ x.dv/dx = v.logv
→ dv/v.logv = dx/x
Let, logv = t
Hence, dv/v = dt
→ dt/t = dx/x
Integrating both sides
→ ln(t) = ln(x) + c
or, t = C.x
→ log(y/x) = C.x
or, y/x = kx
or, y = x.kx
Hope it helps.
Thanks and regards,
Kushagra