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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.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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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.
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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