Consider the initial value problem a. Form the complementary solution to the homogeneous equation. |] + [ c(t)=₁ e^(1) ÿp(t)- e't "-RJ) ++ [4], bt+t -^(-1) e^(-1) b. Construct a particular solution by assuming the form p(t)- a+bt and solving for the undetermined constant vectors a and 6. -[3]. c. Form the general solution ÿ(t) — ÿc(t) + ÿp(t) and impose the initial condition to obtain the solution of the initial value problem. 31 (1) 3/2 (1)
Consider the initial value problem a. Form the complementary solution to the homogeneous equation. |] + [ c(t)=₁ e^(1) ÿp(t)- e't "-RJ) ++ [4], bt+t -^(-1) e^(-1) b. Construct a particular solution by assuming the form p(t)- a+bt and solving for the undetermined constant vectors a and 6. -[3]. c. Form the general solution ÿ(t) — ÿc(t) + ÿp(t) and impose the initial condition to obtain the solution of the initial value problem. 31 (1) 3/2 (1)
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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![Consider the initial value problem
a. Form the complementary solution to the homogeneous equation.
[
Tc (t)=₁
e^(1)
p(t)-
e^t
ÿ'
• − [ ]] ++ [*],
=
bt+t
at-4
+0₂
[
-0^(-1)
b. Construct a particular solution by assuming the form p(t)- a + bt and solving for the undetermined constant vectors a and
e^(-1)
5(0) - [3].
0
c. Form the general solution ÿ(t) — ÿc(t) + ÿp(t) and impose the initial condition to obtain the solution of the initial value problem.
3/₁ (t)
3/2 (1)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F80a185d2-1a05-454a-b6ca-141a15185ee9%2F3a9c24d6-5825-4628-a20f-eaa637b99994%2F5r2uocp_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the initial value problem
a. Form the complementary solution to the homogeneous equation.
[
Tc (t)=₁
e^(1)
p(t)-
e^t
ÿ'
• − [ ]] ++ [*],
=
bt+t
at-4
+0₂
[
-0^(-1)
b. Construct a particular solution by assuming the form p(t)- a + bt and solving for the undetermined constant vectors a and
e^(-1)
5(0) - [3].
0
c. Form the general solution ÿ(t) — ÿc(t) + ÿp(t) and impose the initial condition to obtain the solution of the initial value problem.
3/₁ (t)
3/2 (1)
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