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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 For The Life Sciences
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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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 =
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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Calculus For The Life Sciences
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