A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
pls explain the concept of homogeneous differential equation
anonymous
 4 years ago
pls explain the concept of homogeneous differential equation

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0A homogenous differential equation is something in the form: \[y(t) \left[ \sum_{k=0}^{n} \left( f_n(t) \frac{d^n}{dt^n} \right) \right]=0\] Where f_n(t) is some arbitrary function multiplying the n^th differential operator acting on y(t). A homogenous equation is just one that is equal to zero. For example: \[y''(t)+y'(t)=0\] Or: \[\sin(t)y'(t)+y(t)\cos(3t)e^{2t}=0\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Well, if you have something like: \[y''+3y'+2=0\] You can rewrite it as a polynomial (as something to do with linear algebra and eigenvalues) \[\phi^2+3\phi+2=0 \implies (\phi+2)(\phi+1)=0 \implies \phi=2,1\] So the solution is: \[y(t)=c_1e^{2t}+c_2e^{t}\]
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.