In this problem you will use undetemined coefficients to solve the nonhomogeneous equation y" - 9y = 12te - 14e - (181 +9) with initial values y(0) = -2 and y(0) = 7.
In this problem you will use undetemined coefficients to solve the nonhomogeneous equation y" - 9y = 12te - 14e - (181 +9) with initial values y(0) = -2 and y(0) = 7.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![In this problem you will use undetemined coefficients to solve the nonhomogeneous equation
y" - 9y = 12te - 14e * - (18t + 9)
-31
-3t
with initial values y(0) = -2 and y (0) = 7.
A. Write the characteristic equation for the associated homogeneous equation. (Use r for your variable.)
r^2-9=0
B. Write the fundamental solutions for the associated homogeneous equation.
YI = e^(3")
y2 = [e^(-3"t]
C. Write the form of the particular solution and its derivatives. (Use A, B, C, etc. for undetermined coefficients.
Y =
Y' =
Y" =
D. Write the general solution. (Use c1 and c2 for c, and c2).
y = (e^(-31)"(t^(2) +2t+2(e^{-3t))+(e^(-3t)*c1+(e^(3t)*c2
E. Plug in the initial values and solve for e, and cz to find the solution to the initlal value problem.
y = (e^(31)+2t-(@^(-3t) (t-2)-1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ef4cc44-00f5-4e4f-957e-3112ed5a7b2f%2Fbb729a04-02ad-4499-80cb-85538946d976%2Fdaj1uwv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In this problem you will use undetemined coefficients to solve the nonhomogeneous equation
y" - 9y = 12te - 14e * - (18t + 9)
-31
-3t
with initial values y(0) = -2 and y (0) = 7.
A. Write the characteristic equation for the associated homogeneous equation. (Use r for your variable.)
r^2-9=0
B. Write the fundamental solutions for the associated homogeneous equation.
YI = e^(3")
y2 = [e^(-3"t]
C. Write the form of the particular solution and its derivatives. (Use A, B, C, etc. for undetermined coefficients.
Y =
Y' =
Y" =
D. Write the general solution. (Use c1 and c2 for c, and c2).
y = (e^(-31)"(t^(2) +2t+2(e^{-3t))+(e^(-3t)*c1+(e^(3t)*c2
E. Plug in the initial values and solve for e, and cz to find the solution to the initlal value problem.
y = (e^(31)+2t-(@^(-3t) (t-2)-1
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