ax²y" + bxy' + cy = f(x) (a) Let y1(x) and y2(x) be solutions to the associated homogeneous equation, and let yp(x) be a solution to the non-homogeneous equation. Is y(x) = C1y1(x) +C2y2(x)+Yp(x) the general solution to the non-homogeneous ODE? Prove or provide a counterexample. (b) Solve x²y" + xy' – 9y = 5e2" using any method.
ax²y" + bxy' + cy = f(x) (a) Let y1(x) and y2(x) be solutions to the associated homogeneous equation, and let yp(x) be a solution to the non-homogeneous equation. Is y(x) = C1y1(x) +C2y2(x)+Yp(x) the general solution to the non-homogeneous ODE? Prove or provide a counterexample. (b) Solve x²y" + xy' – 9y = 5e2" using any 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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
Transcribed Image Text:Consider the non-homogeneous Cauchy-Euler equation
ax?y" + bry' + cy = f(x)
(a) Let y1 (x) and y2(x) be solutions to the associated homogeneous equation, and let yp(x)
be a solution to the non-homogeneous equation. Is y(x) = C1y1(x) +C2y2(x)+Yp(x) the
general solution to the non-homogeneous ODE? Prove or provide a counterexample.
(b) Solve x?y" + xy' – 9y = 5e2¤ using any method.
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