Consider the following. Differential Equation Solutions y"" + 6y" +9y' = 0 {e-3x, xe-3x, (3x + 1)e-³x) (a) Verify that each solution satisfies the differential equation. y = e-3x
Consider the following. Differential Equation Solutions y"" + 6y" +9y' = 0 {e-3x, xe-3x, (3x + 1)e-³x) (a) Verify that each solution satisfies the differential equation. y = e-3x
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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Transcribed Image Text:Consider the following.
OCT
29
Differential Equation
Solutions
y"" + 6y" + 9y' = 0 {e-3x, xe-3x, (3x + 1)e-3x}
(a) Verify that each solution satisfies the differential equation.
y = e-3x
y'
y" =
y"" =
y" + 6y" +9y'
=
Y = xe-3x
y' =
y" =
y" = =
y"" + 6y" +9y' =
y = (3x + 1)e-3x
y'
||
y" =
||
A
81
P
Transcribed Image Text:OCT
29
y" + 6y" +9y' =
y"
(b) Test the set of solutions for linear independence.
Olinearly independent
Olinearly dependent
(c) If the set is linearly independent, then write the general solution of the differential equation. (If the system is dependent, enter DEPENDENT. Use C₁ and
C₂ for any needed constants.)
y =
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