y" + 2y' + y = 3t + 9 – (12tet + 2et) with initial values y(0) = 5 and y'(0) = 4. A. Write the characteristic equation for the associated homogeneous equation. (Use r for your variable.) B. Write the fundamental solutions for the associated homogeneous equation. Y1 = Y2 = 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 cCi and c2 to find the solution to the initial value problem. y =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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y" + 2y' + y = 3t +9 – (12tet + 2e*)
with initial values y(0) = 5 and y'(0) = 4.
A. Write the characteristic equation for the associated homogeneous equation. (Use r for your variable.)
B. Write the fundamental solutions for the associated homogeneous equation.
Y1 =
Y2 =
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. Plug in the initial values and solve for cC1 and c2 to find the solution to the initial value problem.
y =
Transcribed Image Text:y" + 2y' + y = 3t +9 – (12tet + 2e*) with initial values y(0) = 5 and y'(0) = 4. A. Write the characteristic equation for the associated homogeneous equation. (Use r for your variable.) B. Write the fundamental solutions for the associated homogeneous equation. Y1 = Y2 = 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. Plug in the initial values and solve for cC1 and c2 to find the solution to the initial value problem. y =
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