, PLEASE USE THIS DOCUMENT AS A GUIDE TO ANSWER YOUR ASSIGNMENT
Question 1
1. Set up the power series for y( x)
Assume the solution can be written as a power series:
00
y(x) =L anx n
n=O
where an are the coefficients to be determined.
2. Find expressions for y' ( x) and y" ( x)
Differentiating the power series term by term:
00
y'(x) = L annxn- l
n= l
00
y"(x) =L ann(n - l )xn- 2
n= 2
3. Substitute these expressions into the differential equation
Substitute y(x), y'(x), and y"(x) into the given equation:
y" - xy' +4y = 2
The equation becomes:
00 00 00
L ann(n - l )xn- 2
- XL annxn- l + 4 L anxn = 2
n=2 n= l
Question 1
1. Set up the power series for y( x)
Assume the solution can be written as a power series:
00
y(x) =L anx n
n=O
where an are the coefficients to be determined.
2. Find expressions for y' ( x) and y" ( x)
Differentiating the power series term by term:
00
y'(x) = L annxn- l
n= l
00
y"(x) =L ann(n - l )xn- 2
n= 2
3. Substitute these expressions into the differential equation
Substitute y(x), y'(x), and y"(x) into the given equation:
y" - xy' +4y = 2
The equation becomes:
00 00 00
L ann(n - l )xn- 2
- XL annxn- l + 4 L anxn = 2
n=2 n= l
