Using the method of indefinite coefficients, solve the following non-homogeneous linear differential equation. y′′+4y=e^(8x) a) Write the characteristic equation of the corresponding homogeneous part of the equation using the variable m. b) Write the homogeneous solution of the equation as yh = c1y1 + c2y2. Write the arbitrary constants c1 and c2 as c1 and c2. The y1 solution must satisfy the condition y1 (0) = 1 and the y2 solution must satisfy the y2 (0) = 0 c) A special solution of the equation A, B, C etc. write using indefinite coefficients. d) Calculate the indeterminate coefficients used, and
Using the method of indefinite coefficients, solve the following non-homogeneous linear differential equation. y′′+4y=e^(8x) a) Write the characteristic equation of the corresponding homogeneous part of the equation using the variable m. b) Write the homogeneous solution of the equation as yh = c1y1 + c2y2. Write the arbitrary constants c1 and c2 as c1 and c2. The y1 solution must satisfy the condition y1 (0) = 1 and the y2 solution must satisfy the y2 (0) = 0 c) A special solution of the equation A, B, C etc. write using indefinite coefficients. d) Calculate the indeterminate coefficients used, and
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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Using the method of indefinite coefficients, solve the following non-homogeneous linear
y′′+4y=e^(8x)
a) Write the characteristic equation of the corresponding homogeneous part of the equation using the variable m.
b) Write the homogeneous solution of the equation as yh = c1y1 + c2y2. Write the arbitrary constants c1 and c2 as c1 and c2. The y1 solution must satisfy the condition y1 (0) = 1 and the y2 solution must satisfy the y2 (0) = 0
c) A special solution of the equation A, B, C etc. write using indefinite coefficients.
d) Calculate the indeterminate coefficients used, and write down the specific solution obtained: yp =?
e) Finally write the general solution: y =?
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