Consider the differential equation y" - 25y = 25x e-5z Use coefficients c₁ and ₂ if needed. Use exp(x) for the exponential function. (a) find one solution of the homogeneous equation: 3h (2) c1e^(5x)+c2e^-5x (b) find a particular solution to the nonhomogeneous equation using the variation of parameters formula: y₂(z)=(5/4)x^(2)(e^(5x))(-5/x)[(10xe^(10x))(-e)^(10x)/(100)]
Consider the differential equation y" - 25y = 25x e-5z Use coefficients c₁ and ₂ if needed. Use exp(x) for the exponential function. (a) find one solution of the homogeneous equation: 3h (2) c1e^(5x)+c2e^-5x (b) find a particular solution to the nonhomogeneous equation using the variation of parameters formula: y₂(z)=(5/4)x^(2)(e^(5x))(-5/x)[(10xe^(10x))(-e)^(10x)/(100)]
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
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 5E
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![Consider the differential equation
y" - 25y =
25x
e-5z'
Use coefficients c₁ and c₂ if needed.
Use exp(x) for the exponential function.
(a) find one solution of the homogeneous equation:
yh(x)
= c1e^(5x)+c2e^-5x
(b) find a particular solution to the nonhomogeneous equation using the variation of parameters formula:
yp(x)=
(5/4)x^(2)(e^(5x))(-5/x)[(10xe^(10x))(-e)^(10x)/(100)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ca59a39-6147-4a43-b981-39fc71e0e26c%2F2b2bcdec-e67a-4230-80cd-bbba4dbcda63%2Fym1yck_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the differential equation
y" - 25y =
25x
e-5z'
Use coefficients c₁ and c₂ if needed.
Use exp(x) for the exponential function.
(a) find one solution of the homogeneous equation:
yh(x)
= c1e^(5x)+c2e^-5x
(b) find a particular solution to the nonhomogeneous equation using the variation of parameters formula:
yp(x)=
(5/4)x^(2)(e^(5x))(-5/x)[(10xe^(10x))(-e)^(10x)/(100)]
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