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Question

Solve differential equation :
xlogxdydx+y=2logx

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Solution

xlogxdydx+y=2logx
divide throughout with xlogx
dydx+yxlogx=2x
dydx+y(f(x))=g(x)
Linear differential
Integrating factor ef(x)dx
=e1xlogxdx
logx=t1xdx=dt
=edtt=elnt=t
=logx
IF=logx
y×(IF)=(IF)g(x)dx+c
ylogx=logx(2)xdx+c logx=p1dxdx=dp
ylogx=2pdp+c
ylogx=p2+c
ylogx=(log)2+c
y=logx+clogx.

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