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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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 =
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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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,