home > q&a board > calculus > topic: reduce the third order equation

Q BgQuestion:

Pupil
Karma Points: 51
Respect (94%):
posted by  pike on 7/24/2008 10:42:55 AM  |  status: Live  

Reduce the third order equation

Course Textbook Chapter Problem
Differential Equations N/A N/A N/A
Question Details:
Reduce the third order equation y ''' - 3y '' + 6y' -10y = t2  +1 to the normal form

AAnswers:

Answer Question
Sage
Karma Points: 4,209
posted by stejaes on 8/11/2008 10:18:04 AM  |  status: Live
Asker's Rating: This answer has not been rated. If you asked this question, then please login.   
Response Details:
A particular solution is yparticular(t)=(-28-30t-25t2)/250. A polynomial trial function. Since only y can compensate for t2, this coefficient must be -1/10. The linear coefficients have to vanish: -6/5-6/5 from the first derivativ compensate that from y. 3/5-18/25+28/25=1 for the constant.
 
The solution of the homogeneous equation is the linear combination of the exponential function with the roots of the characteristic equation a exponential coefficients.
 
The roots are
x2/3=1+(1+i√3)/(2(3+√10)1/3)-(1±i√3)(3+√10)1/3/2.
Answer Question
Ask New Question

Join Cramster's Community

Cramster.com brings together students, educators and subject enthusiasts in an online study community. With around-the-clock expert help and a community of over 100,000 knowledgeable members, you can find the help you need, whenever you need it. Join for free today »

Need Help In

Useful Links