In this problem you will use undetemined coefficients to solve the nonhomogeneous equationy" - 9y = 12te - 14e * - (18t + 9)-31-3twith initial values y(0) = -2 and y (0) = 7.A. Write the characteristic equation for the associated homogeneous equation. (Use r for your variable.)r^2-9=0B. Write the fundamental solutions for the associated homogeneous equation.YI = e^(3")y2 = [e^(-3"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 c, and c2).y = (e^(-31)"(t^(2) +2t+2(e^{-3t))+(e^(-3t)*c1+(e^(3t)*c2E. Plug in the initial values and solve for e, and cz to find the solution to the initlal value problem.y = (e^(31)+2t-(@^(-3t) (t-2)-1

Answered: In this problem you will use…

In this problem you will use undetemined coefficients to solve the nonhomogeneous equation y" - 9y = 12te - 14e - (181 +9) with initial values y(0) = -2 and y(0) = 7.

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

In this problem you will use undetemined coefficients to solve the nonhomogeneous equation
y" - 9y = 12te - 14e * - (18t + 9)
-31
-3t
with initial values y(0) = -2 and y (0) = 7.
A. Write the characteristic equation for the associated homogeneous equation. (Use r for your variable.)
r^2-9=0
B. Write the fundamental solutions for the associated homogeneous equation.
YI = e^(3")
y2 = [e^(-3"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 c, and c2).
y = (e^(-31)"(t^(2) +2t+2(e^{-3t))+(e^(-3t)*c1+(e^(3t)*c2
E. Plug in the initial values and solve for e, and cz to find the solution to the initlal value problem.
y = (e^(31)+2t-(@^(-3t) (t-2)-1

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