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MATH308: Quiz 5 Solution - Solving a Differential Equation, Quizzes of Differential Equations

Texas A&M University (A&M)Differential Equations

The solution to quiz 5 question of math308 course, which involves setting up and solving a differential equation using the characteristic equation and finding the general solution form. The given differential equation, the characteristic equation, and the solution form.

Typology: Quizzes

2019/2020

Uploaded on 11/25/2020

koofers-user-tnq
koofers-user-tnq 🇺🇸

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MATH308: Quiz 5
1. (10 points) Set up the solution form for '' 2 ' 2 sin
t
y
yyte
−
++= t
0
The characteristic equation is 222rr
+
+=
The solution to is
222rr++=01,2 1ri
=
−±.
Since 1
1iir
γ
η
+=−+=, s=1
The solution form of the differential equation is {( ) sin ( ) cos }
tt
tAtBe t CtDe t
−−
+++

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MATH308: Quiz 5

  1. (10 points) Set up the solution form for y '' + 2 y '+ 2 y = te − t sin t The characteristic equation is r^2 + 2 r + 2 = 0 The solution to is 2 r + 2 r + 2 = 0 r 1,2 (^) = − ± 1 i.

Since γ + η i = − + 1 i = r 1 , s=

The solution form of the differential equation is {( ) sin ( ) cos } t t t At B e t Ct D e t − −