Differential equation by method of power series: (x-2)y'' - (x+1)y' - (x-2)y = 0

[ticou]

Can anyone solve this differential equation by the power series method?


(x-2)y'' - (x+1)y' - (x-2)y = 0


Subject to initial conditions: y(0)= -1 ,
y'(0)= 1


Compute the first four non-zero terms and, if possible, find the general term of each series.


thanks!

 

[mmm4444bot]

Hi. This is a tutoring web site. What have you tried or thought about, in this exercise, so far? Where did you get stuck?

Also, please read the forum guidelines, before posting again. Thank you! :cool:

 

[ticou]

Hi. This is a tutoring web site. What have you tried or thought about, in this exercise, so far? Where did you get stuck?

Also, please read the forum guidelines, before posting again. Thank you! :cool:

I came up with a result is a second order equation but not by the power series method


y=C1e^[-1/2(sqt5-1)(x-2)][(x-2)^4][5/2+(2/2sqt5)]+C2e^[-1/2(sqt5-1)(x-2)][(x-2)^4][5/2-(2/2sqt5)(sqt5)()x-2]