Thread Closed

differential equation problem

 
Share Thread Thread Tools
May28-05, 10:59 AM   #1
 

differential equation problem


i'm trying to find what the intermediate steps were used in solving this differential equation:

[tex]y'' + y' -3y =0[/tex]

[tex]m=\frac{-1\pm\sqrt{13}}{2}[/tex] now we have

[tex]y=C_1e^{\frac{-.5+\sqrt{13}}{2}}t + C_2e^{\frac{-.5 -\sqrt{13}}{2}}t[/tex]

note that the .5 are 1\2. i couldn't get the latex for this to work
PhysOrg.com
PhysOrg
science news on PhysOrg.com

>> King Richard III found in 'untidy lozenge-shaped grave'
>> Google Drive sports new view and scan enhancements
>> Researcher admits mistakes in stem cell study
May28-05, 11:01 AM   #2
 
Recognitions:
Gold Membership Gold Member
Homework Helper Homework Help
Science Advisor Science Advisor
Do you know where "m" came from?
May28-05, 11:11 AM   #3
 
Quote by arildno
Do you know where "m" came from?

that m came from the auxillary equation of the differential
[tex]r^2 +r -3=0[/tex]
May28-05, 11:15 AM   #4
 
Recognitions:
Gold Membership Gold Member
Homework Helper Homework Help
Science Advisor Science Advisor

differential equation problem


So what's bugging you, then?
May28-05, 04:40 PM   #5
 
Recognitions:
Gold Membership Gold Member
Homework Helper Homework Help
Science Advisor Science Advisor
Quote by RadiationX
i'm trying to find what the intermediate steps were used in solving this differential equation:

[tex]y'' + y' -3y =0[/tex]

[tex]m=\frac{-1\pm\sqrt{13}}{2}[/tex] now we have

[tex]y=C_1e^{\frac{-.5+\sqrt{13}}{2}}t + C_2e^{\frac{-.5 -\sqrt{13}}{2}}t[/tex]

note that the .5 are 1\2. i couldn't get the latex for this to work
As you noted, you created the auxiliary (or characteristic) equation. The auxiliary equation was solved via the quadratic formula.

Note: You should have:
[tex]y=C_1e^{(-.5 + \frac{\sqrt{13}}{2})t} + C_2e^{(-.5-\frac{\sqrt{13}}{2})t}[/tex]
May29-05, 12:09 PM   #6
 
Recognitions:
Gold Membership Gold Member
Science Advisor Science Advisor
Retired Staff Staff Emeritus
If you were wondering where the characteristic equation came from, assume a solution ofthe form y= ert, plug it into the differential equation and see what r must be in order to make the equation true.
Thread Closed
Thread Tools


Similar Threads for: differential equation problem
Thread Forum Replies
Serious problem about Differential equation Differential Equations 2
Differential Equation Problem? Calculus & Beyond Homework 5
Differential equation problem Calculus & Beyond Homework 1
Differential equation problem Calculus & Beyond Homework 1
Differential equation problem Introductory Physics Homework 4