y"+P(x)y'+Z(x)y=0

is second order homogeneous differential equation. if yp is particular solution then y=yp.u, we can transform u into first order differential equation.

If m(m-1)+mxP(x)+Q(x)x^{2}=0, yparticular=x^{m}

if m^{2}+mP(x)+Q(x)=0, yparticular=e^{mx}

question: 1.(x-1)y"-xy'+y=0, find y

the answer on the book said that m^{2}(x-1)-mx+1=(m-1)(mx-m-1)=0. m=1 and yp= e^{x}can someone explain how to get this?? thanks!

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