Use Euler's method with step sizes h = 0.1 and h = 0.05 to find approximate values of the solution of the initial value problem: y′ + 2y = x^3(e^−2x), y(0) = 7 at x = 0, 0.1, and 1.0 Compare these approximate values with the values of the exact solution: y = [e^(−2x/4)](x^4 + 4) Hint: Verify this exact solution by Linear 1st order solution method.
Use Euler's method with step sizes h = 0.1 and h = 0.05 to find approximate values of the solution of the initial value problem: y′ + 2y = x^3(e^−2x), y(0) = 7 at x = 0, 0.1, and 1.0 Compare these approximate values with the values of the exact solution: y = [e^(−2x/4)](x^4 + 4) Hint: Verify this exact solution by Linear 1st order solution method.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use Euler's method with step sizes h = 0.1 and h = 0.05 to find approximate values of the solution of the initial value problem:
y′ + 2y = x^3(e^−2x), y(0) = 7 at x = 0, 0.1, and 1.0
Compare these approximate values with the values of the exact solution:
y = [e^(−2x/4)](x^4 + 4)
Hint: Verify this exact solution by Linear 1st order solution method.
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