Differential equations and series

[freshman2013]

1.

1.Homework Statement

Use power series to evaluate intial value problem y''-xy'-2y=4x^2 y(0)=1 and y'(0)=1

Homework Equations

The Attempt at a Solution

I got the series Cnx^n and took its derivative and plugged it into the formula and I got but when I factor out x^n and set that experssion equal to 4x^2, I realize I'm stuck and I'm not sure If I'm doing it correctly.

 

[pasmith]

1.

1.Homework Statement

Use power series to evaluate intial value problem y''-xy'-2y=4x^2 y(0)=1 and y'(0)=1

Homework Equations

The Attempt at a Solution

I got the series Cnx^n and took its derivative and plugged it into the formula and I got but when I factor out x^n and set that experssion equal to 4x^2, I realize I'm stuck and I'm not sure If I'm doing it correctly.

What that tells you is that coefficient of x^2 on the left hand side is 4, and the coefficient of every other power of x on the left hand side is zero.