A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
for what values of the (real) constants a and b all solutions of the equations y"+ay'+by=0, are bounded for x between minus infinity and infinity?
anonymous
 5 years ago
for what values of the (real) constants a and b all solutions of the equations y"+ay'+by=0, are bounded for x between minus infinity and infinity?

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Solve for the solution to the differential equation generally. Use the characteristic equation (e^(rx) substitution results). You should get the quadratic equation.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0helpme, i dont really get it. could u plis explain more in detail?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0That's a differential equation. You have to solve it. There are many different methods to determine the solutions. One of them is by substituting e^(rx) into the solution. You'll realize, that after you plug in the equation, that the e^(rx) divides into the zero. That leaves you with R^2+aR+b=0, which is a simple equation to solve. Just use the quadratic formula, with a and b as your coefficients. Later on, you substitute the solution back into your formula.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0helpmeplease is right, the Characteristic equation is\[r^2+ar+b=0\] so the roots are:\[r_{1}=\frac{a+\sqrt{a^24b}}{2}, r_{2}=\frac{a\sqrt{a^24b}}{2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0after get the roots, differentiate the solution then substitute them into y",y' and y in the original equation?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if the roots are real distinct roots use: \[y=C_{1}e^{r_{1}x}+C_{1}e^{r_{2}x}\] If the roots are real and repeated where r1=r2 use: \[y=C_{1}xe^{r_{1}x}+C_{1}e^{r_{2}x}\] If the roots are Complex then use: \[\lambda=\frac{a}{2}, \mu i=\pm \frac{\sqrt{a^24b}}{2}i\] \[y=e^{\lambda x}C_{1}\cos(\mu x)+e^{\lambda x}C_{2}\sin(\mu x)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thanks nadeem and helpmeplease
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.