Consider the non-homogeneous third order equation y''' − 4y'' + 5y' − 2y = 30 e^t . A. Find a fundamental set of solutions y1, y2, y3 of the associated homogeneous equation y''' − 4y'' + 5y' − 2y = 0. B. Compute the Wronskian W = W(y1, y2, y3) for the three functions y1, y2, y3 found in part A. C. Check Abel’s Formula by determining the value of α. D. Find a particular solution Y (t) of the original non-homogeneous equation using the method of undetermined coefficients
Consider the non-homogeneous third order equation y''' − 4y'' + 5y' − 2y = 30 e^t . A. Find a fundamental set of solutions y1, y2, y3 of the associated homogeneous equation y''' − 4y'' + 5y' − 2y = 0. B. Compute the Wronskian W = W(y1, y2, y3) for the three functions y1, y2, y3 found in part A. C. Check Abel’s Formula by determining the value of α. D. Find a particular solution Y (t) of the original non-homogeneous equation using the method of undetermined coefficients
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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Consider the non-homogeneous third order equation
y''' − 4y'' + 5y' − 2y = 30 e^t .
A. Find a fundamental set of solutions y1, y2, y3 of the associated homogeneous equation y''' − 4y'' + 5y' − 2y = 0.
B. Compute the Wronskian W = W(y1, y2, y3) for the three functions y1, y2, y3 found in part A.
C. Check Abel’s Formula by determining the value of α.
D. Find a particular solution Y (t) of the original non-homogeneous equation using the method of undetermined coefficients.
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