In this problem you will use undetermined coefficients to solve the nonhomogeneous equation "+6y+9y=6te-3t with initial values y(0) = =-2 and '(0) = 2. +18t+3 A. Write the characteristic equation for the associated homogeneous equation. (User for your variable.) B. Write the fundamental solutions for the associated homogeneous equation. 31 = 32= 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 c₁ and c₂). У E. Plug in the initial values and solve for c₁ and c₂ to find the solution to the initial value problem. y= Hint: No fractions are required in the solution or answer to this problem.
In this problem you will use undetermined coefficients to solve the nonhomogeneous equation "+6y+9y=6te-3t with initial values y(0) = =-2 and '(0) = 2. +18t+3 A. Write the characteristic equation for the associated homogeneous equation. (User for your variable.) B. Write the fundamental solutions for the associated homogeneous equation. 31 = 32= 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 c₁ and c₂). У E. Plug in the initial values and solve for c₁ and c₂ to find the solution to the initial value problem. y= Hint: No fractions are required in the solution or answer to this problem.
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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Transcribed Image Text:In this problem you will use undetermined coefficients to solve the nonhomogeneous equation
"+6y+9y=6te-3t
with initial values y(0) =
=-2 and '(0) = 2.
+18t+3
A. Write the characteristic equation for the associated homogeneous equation. (User for your
variable.)
B. Write the fundamental solutions for the associated homogeneous equation.
31 =
32=
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 c₁ and c₂).
У
E. Plug in the initial values and solve for c₁ and c₂ to find the solution to the initial value
problem.
y=
Hint: No fractions are required in the solution or answer to this problem.
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