Power Series

[JeffChris]

Can someone please help on this? Really urgent.
Find the power series solutions around x = − 1 for the following differential equation (x + 1) y" + 3x y' − y = 0?

Thank you.

 

[stapel]

Can someone please help on this? Really urgent.
Find the power series solutions around x = − 1 for the following differential equation (x + 1) y" + 3x y' − y = 0?

At what point in the process are you getting stuck? Please be specific, showing all of your work leading up to that point. Thank you!

 

[JeffChris]

I couldn't even start. I was only taught to solve power series around x=0.

 

[Deleted member 4993]

Can someone please help on this? Really urgent.
Find the power series solutions around x = − 1 for the following differential equation (x + 1) y" + 3x y' − y = 0?

Thank you.

Substitute

z = x +1

Then do the power series about z = 0 → x = -1

Then substitute back....

 

[JeffChris]

Thank you very much sir

 

[HallsofIvy]

Substitute

z = x +1

Then do the power series about z = 0 → x = -1

Then substitute back....

Equivalently, write y as a power series in x+ 1: \(\displaystyle y= \sum_{n= 0}^\infty a_n(x+ 1)^n\).