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I got this book from WILEY by Erwin Kreyszig. It tells how to solved homogenous cauchy equations. It also covers simple nonhomogenous equations.

But it doesn't cover when we have nonhomogenous Cauchy equations like this one.

x2y''-xy'+y=lnx

How do I go about solving that equation?

I substituted x=e ^t and obtained the homogeneous solution yh=c1*x+c2*x

but there is still the partial solution (yp).

Any idea?

final answer should be y=yh+yp

But it doesn't cover when we have nonhomogenous Cauchy equations like this one.

x2y''-xy'+y=lnx

How do I go about solving that equation?

I substituted x=e ^t and obtained the homogeneous solution yh=c1*x+c2*x

but there is still the partial solution (yp).

Any idea?

final answer should be y=yh+yp

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