# Thread: cauchy uler differential equation: y" + P(x) y' + Z(x) y = 0

1. ## cauchy uler differential equation: y" + P(x) y' + Z(x) y = 0

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)x2 =0, yparticular=xm
if m2+mP(x)+Q(x)=0, yparticular=emx
question: 1.(x-1)y"-xy'+y=0, find y

the answer on the book said that m2(x-1)-mx+1=(m-1)(mx-m-1)=0. m=1 and yp= ex can someone explain how to get this?? thanks!

2. Originally Posted by devinamuljono
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)x2 =0, yparticular=xm
if m2+mP(x)+Q(x)=0, yparticular=emx
question: 1.(x-1)y"-xy'+y=0, find y

the answer on the book said that m2(x-1)-mx+1=(m-1)(mx-m-1)=0. m=1 and yp= ex can someone explain how to get this?? thanks!

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

http://www.freemathhelp.com/forum/announcement.php?f=33

3. Originally Posted by devinamuljono
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)x2 =0, yparticular=xm
if m2+mP(x)+Q(x)=0, yparticular=emx
question: 1.(x-1)y"-xy'+y=0, find y

the answer on the book said that m2(x-1)-mx+1=(m-1)(mx-m-1)=0. m=1 and yp= ex can someone explain how to get this?? thanks!
Please specify at what point the book's explanation stopped making sense. Thank you!