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Question
For the differential equation, find the general solution:
y log y dx - x dy = 0
Solution
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.
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