Power Series Approximation of an IVP

Click For Summary
The discussion focuses on finding the first four nonzero terms of the power series approximation for the initial value problem defined by the differential equation y'' - 4y = 4t - 8e^(-2t) with initial conditions y(0) = 1 and y'(0) = -1. Participants express confusion regarding the transition from a homogeneous to a non-homogeneous equation, particularly in deriving coefficients for the power series. Recursive formulas have been established, but most terms result in zero, prompting questions about the correct approach to derive non-zero coefficients. Clarification is sought on the methodology for obtaining these coefficients in the context of the given equation. The discussion emphasizes the challenge of handling non-homogeneous terms in power series solutions.
LUMath2012
Messages
1
Reaction score
0
1. Find the first four nonzero terms of the power series approximation of the solution.
y"-4y = 4t-8e-2t y(0)=1, y'(0)=-1


2. y=\suma_n*t^n where the summation goes from 0 to infinity



3. I have done a homogeneous problem similar to this and had no problems finding the first four terms. However, I am confused as far as where to go with the non-homogeneous equation. I have recursive formulas for the first four terms but all of them but one end up being equal to 0. Just wondering where I go from here.
 
Last edited:
Physics news on Phys.org
how did you derive your formulas for the coefficients?
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

Avoid unpleasant integrals in solving IVP
  • · Replies 3 ·
Replies
3
Views
2K
On the ratio test for power series
  • · Replies 2 ·
Replies
2
Views
2K
Multiplication of Taylor and Laurent series
  • · Replies 12 ·
Replies
12
Views
3K
Series Solution to Second Order DE
  • · Replies 5 ·
Replies
5
Views
2K
Finding 2 solutions of this Bessel's function using a power series
  • · Replies 8 ·
Replies
8
Views
2K
Solving a Gaussian integral using a power series?
  • · Replies 9 ·
Replies
9
Views
3K
How to show that these sequences are summable?
  • · Replies 1 ·
Replies
1
Views
2K
Diff. Eq. — Identifying Particular Solution Given solution family
  • · Replies 4 ·
Replies
4
Views
2K
How should I show that this root is given approximately by this?
  • · Replies 2 ·
Replies
2
Views
2K
Differential equation with power series method
  • · Replies 4 ·
Replies
4
Views
2K