Solution Found!
Solution: As in Exercises 3.6, for some problems you will
Chapter 3, Problem 5E(choose chapter or problem)
Use the Taylor methods of orders 2 and 4 with \(h=0.25\) to approximate the solution to the initial value problem
\(y{\prime}=x+1-y\), \(y(0)=1\),
at \(x=1\). Compare these approximations to the actual solution \(y=x+e^{-x}\) evaluated at \(x=1\).
Equation Transcription:
Text Transcription:
h=0.25
y{\prime}=x+1-y
y(0)=1
x=1
y=x+e^{-x}
x=1
Questions & Answers
QUESTION:
Use the Taylor methods of orders 2 and 4 with \(h=0.25\) to approximate the solution to the initial value problem
\(y{\prime}=x+1-y\), \(y(0)=1\),
at \(x=1\). Compare these approximations to the actual solution \(y=x+e^{-x}\) evaluated at \(x=1\).
Equation Transcription:
Text Transcription:
h=0.25
y{\prime}=x+1-y
y(0)=1
x=1
y=x+e^{-x}
x=1
ANSWER:
Solution:
Step 1
In this problem we need to find the recursive formula for the taylor series of order 4 for the given initial value problem.