Question

For the differential equation, find the general solution:

y log y dx - x dy = 0

Answer 1

y log y dx - x dy = 0

dividing by xy log y

`dx/x - 1/(y log y)  dy = 0`

or `int dx/x - int 1/(y log y)  dy = 0`

Putting `log y = t`, `1/y dy = dt`

`therefore log x - int 1/t  dt = 0`

or  `log t = log x + log C`

either `log  abs(log y) = log Cx`

`=>  log y = Cx`

`therefore y = e^(Cx)` which is the required solution.