Constructing a DE

  • #1
Hi

I'm working through some example question and the memo leaves out this question. I was hoping someone can help me out.

The question:
Construct a differential equation of the form y'' + by' + cy = 0 which has y(t) = e^t cos(3t) as one of its solutions.

What I did:
First I found the y'(t) and y''(t)
Plugged that into the DE.

My answer:
b = -2
c = -6

y'' - 2y' - 6y = 0
 

Answers and Replies

  • #2
Simon Bridge
Science Advisor
Homework Helper
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Check your answer by plugging the solution into it from scratch.
It will also help to show your working step-by-step.
 
  • #3
35,919
12,745
You can use WolframAlpha to check your result.
 
  • #4
pasmith
Homework Helper
2,205
809
Hi

I'm working through some example question and the memo leaves out this question. I was hoping someone can help me out.

The question:
Construct a differential equation of the form y'' + by' + cy = 0 which has y(t) = e^t cos(3t) as one of its solutions.

What I did:
First I found the y'(t) and y''(t)
Plugged that into the DE.

My answer:
b = -2
c = -6

y'' - 2y' - 6y = 0

Hint: What is the relationship between the ODE
[tex]
y'' + by' + cy = 0
[/tex]
and the quadratic equation
[tex]
\lambda^2 + b\lambda + c = 0?
[/tex]

You may also find the identity
[tex]
\cos kt \equiv \frac{e^{ikt} + e^{-ikt}}{2}
[/tex]
helpful.
 

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