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

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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: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
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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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 = Submit Answer % MacBook Air A P TR
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