Question

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

Solution

Integrating factor of dydx+Py=Q is e∫Pdx Converting xlogxdydx+y=2logx in standard form, we get dydx+yxlogx=2x So, integrating factor is e∫1xlogxdx Solving further: Let logx=t ⇒1xdx=dt Integrating factor becomes e∫1tdt e∫1tdt=elogt=t=logx So, integrating factor of the given differential equation is logx.Mathematics

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