In this problem you will use undetermined coefficients to solve the nonhomogeneous equation y"-y=4e¹-4te + 3t-2 with initial values y(0) = 2 and y'(0) = -2. A. Write the characteristic equation for the associated homogeneous equation. (User for your variable.) M^2-1=0 B. Write the fundamental solutions for the associated homogeneous equation. 31=e^t 3/2 = e^(-1) 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). y= E. Plug in the initial values and solve for c₁ and ₂ to find the solution to the initial value problem. y =
In this problem you will use undetermined coefficients to solve the nonhomogeneous equation y"-y=4e¹-4te + 3t-2 with initial values y(0) = 2 and y'(0) = -2. A. Write the characteristic equation for the associated homogeneous equation. (User for your variable.) M^2-1=0 B. Write the fundamental solutions for the associated homogeneous equation. 31=e^t 3/2 = e^(-1) 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). y= E. Plug in the initial values and solve for c₁ and ₂ to find the solution to the initial value problem. y =
Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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Transcribed Image Text:with initial values y(0) = 2 and y'(0) = -2.
In this problem you will use undetermined coefficients to solve the nonhomogeneous equation
y"-y=4e4tet +3t-2
A. Write the characteristic equation for the associated homogeneous equation. (User for your variable.)
r^2-1=0
B. Write the fundamental solutions for the associated homogeneous equation.
3/₁ = e^t
3/2 = e^(-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 C₁ and C₂).
y =
E. Plug in the initial values and solve for C₁ and c₂ to find the solution to the initial value problem.
y =
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