y\ln x-xy'=0?

Juan Hewlett 2021-12-13 Answered
ylnxxy=0?
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Expert Answer

Raymond Foley
Answered 2021-12-14 Author has 39 answers
ylnxxyylnx=xdydxdyy=lnxxdx
dyy=lnxxdx
ln|y|=ln2x2+C
eln|y|=eln2x2+C
|y|=eln2x2×eCeC=c1
y=celn2x2
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Daniel Cormack
Answered 2021-12-15 Author has 34 answers
lnxxdx
Let lnx=u
thus, we have
dxx=du
lnxxdx=udu
=u22+C
=ln2x2+C
Therefore, y=celn2x2 is the solution
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