SOLUTION: Obtain the general solution y lnx lny dx + dy = 0

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Question 456139: Obtain the general solution
y lnx lny dx + dy = 0
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Divide both sides by ylny, to get
lnx+dx+%2B+dy%2F%28ylny%29+=+0.
<==> lnx+dx+%2B+d%28lny%29%2Flny+=+0
Integrate both sides:
int%28lnx%2C+dx%29+%2B+int%281%2Flny%2C+d%28lny%29%29+=+k k an arbitrary constant.
After integration by parts (on the first integral), the equation becomes
xlnx - x + ln(lny) = k.
Simplifying:
ln%28x%5Ex%29+%2B+ln%28lny%29+=+x%2Bk
<==> ln%28yx%5Ex%29+=+x%2Bk
<==> yx%5Ex+=+e%5E%28x%2Bk%29
<==> yx%5Ex+=+Ce%5Ex <==> y+=+C%28e%2Fx%29%5Ex, where C is an arbitrary constant.