Consider the differential equation у" - у'- 30у 3D 0. Verify that the functions e-5x and e6x form a fundamental set of solutions of the differential equation on the interval (-0, 0). The functions satisfy the differential equation and are linearly independent since the Wronskian We-Sx, e6x) = * 0 for -0 < x < 0. Form the general solution. y =
Consider the differential equation у" - у'- 30у 3D 0. Verify that the functions e-5x and e6x form a fundamental set of solutions of the differential equation on the interval (-0, 0). The functions satisfy the differential equation and are linearly independent since the Wronskian We-Sx, e6x) = * 0 for -0 < x < 0. Form the general solution. y =
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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Question
![Consider the differential equation
y" – y' – 30y = 0.
Verify that the functions e-5x and ebx form a fundamental set of solutions of the differential equation on the interval (-∞, ∞).
The functions satisfy the differential equation and are linearly independent since the Wronskian We
+ 0 for -0 < x < ∞,
Form the general solution.
y =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc08bab33-dfc3-4475-87c9-eef4dfb69a19%2F60fa6606-fb47-464e-a2e0-7fa4b7bfeb3c%2Fj5bjj3f_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the differential equation
y" – y' – 30y = 0.
Verify that the functions e-5x and ebx form a fundamental set of solutions of the differential equation on the interval (-∞, ∞).
The functions satisfy the differential equation and are linearly independent since the Wronskian We
+ 0 for -0 < x < ∞,
Form the general solution.
y =
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