Solution Found!
Use numerical integration (such as Simpson’s rule,
Chapter 2, Problem 26E(choose chapter or problem)
Use numerical integration (such as Simpson’s rule, Appendix C) to approximate the solution, at \(x=1\), to the initial value problem
\(\frac{d y}{d x}+\frac{\sin 2 x}{2\left(1+\sin ^{2} x\right)} y=1\), \(y(0)=0\)
Ensure your approximation is accurate to three decimal places.
Equation Transcription:
Text Transcription:
x=1
{dy}over{dx}+{sin 2x} over {2(1+sin^{2} x)} y=1
y(0)=0
Questions & Answers
QUESTION:
Use numerical integration (such as Simpson’s rule, Appendix C) to approximate the solution, at \(x=1\), to the initial value problem
\(\frac{d y}{d x}+\frac{\sin 2 x}{2\left(1+\sin ^{2} x\right)} y=1\), \(y(0)=0\)
Ensure your approximation is accurate to three decimal places.
Equation Transcription:
Text Transcription:
x=1
{dy}over{dx}+{sin 2x} over {2(1+sin^{2} x)} y=1
y(0)=0
ANSWER:
Solution:
Step 1:
In this problem we have to that the integrating factor for the differential equation can be written as