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Question

Find the integrating factor for the following differential equation :
xlogxdydx+y=2logx


Solution

Integrating factor of dydx+Py=Q is ePdx
Converting xlogxdydx+y=2logx in standard form, we get
dydx+yxlogx=2x
So, integrating factor is e1xlogxdx
Solving further:
Let logx=t
1xdx=dt
Integrating factor becomes e1tdt
e1tdt=elogt=t=logx
So, integrating factor of the given differential equation is logx.

Mathematics

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