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In this problem you will use undetermined coefficients to solve the nonhomogeneous equation y" – 5y' + 6y = 5e* 6tet + 16 – 12t with initial values y(0) -2 and y'(0) = -8. 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. Y2 = C. Write the form of the particular solution and its derivatives. (Use A, B, C, etc. for undetermined coefficients. Y' = Y" = D. Write the general solution. (Use c1 and c2 for c and c2). E. Plug in the initial values and solve for c and c2 to find the solution to the initial value problem. 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 y" – 5y' + 6y = 5e* 6tet + 16 – 12t with initial values y(0) -2 and y'(0) = -8. 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. Y2 = C. Write the form of the particular solution and its derivatives. (Use A, B, C, etc. for undetermined coefficients. Y' = Y" = D. Write the general solution. (Use c1 and c2 for c and c2). E. Plug in the initial values and solve for c and c2 to find the solution to the initial value problem. Hint: No fractions are required in the solution or answer to this problem.

Advanced Engineering Mathematics
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 undetermined coefficients to solve the nonhomogeneous equation y" – 5y' + 6y = 5e* 6tet + 16 – 12t with initial values y(0) -2 and y'(0) = -8. 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. Y2 = C. Write the form of the particular solution and its derivatives. (Use A, B, C, etc. for undetermined coefficients. Y' = Y" = D. Write the general solution. (Use c1 and c2 for c and c2). E. Plug in the initial values and solve for c and c2 to find the solution to the initial value problem. Hint: No fractions are required in the solution or answer to this problem.
Transcribed Image Text:In this problem you will use undetermined coefficients to solve the nonhomogeneous equation y" – 5y' + 6y = 5e* 6tet + 16 – 12t with initial values y(0) -2 and y'(0) = -8. 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. Y2 = C. Write the form of the particular solution and its derivatives. (Use A, B, C, etc. for undetermined coefficients. Y' = Y" = D. Write the general solution. (Use c1 and c2 for c and c2). E. Plug in the initial values and solve for c and c2 to find the solution to the initial value problem. Hint: No fractions are required in the solution or answer to this problem.
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