High order differential equations: undetermined coefficients

  • #1
32
1

Homework Statement



If the method of undetermined coefficients is used to find a particular solution
yp (t) to the differential equation y'''-y'=te^(-t)+2cos(t) should
have the form: ?


Homework Equations




The Attempt at a Solution


LHS

r^3-r=0

roots= 0, 1

y_c(t)=c_1e^t


RHS

te^(-t)+2cos(t)

(At+B)e^(-t)+Ccos(t)+Dsin(t)

correct answer given however is

t(At + B)e^(-t) + C cos(t) + D sin(t)

I don't know how that t in front got there.. It would make sense if my LHS gave e^-t. but i dont think it does.


Thanks
 

Answers and Replies

  • #2
dwn
165
2
Hello dmoney,

Your LHS should be yc(t) = c1et + c2e(0*t) = c1et + c2

missed that .... c3e-t
 
  • #3
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
12,798
1,670
Your characteristic equation is third order in r. How many roots are there?
 
  • #4
32
1
Your characteristic equation is third order in r. How many roots are there?

right... 3 roots...

so r^3-r=0

r=0, r=1, and.... r=-1

-1-(-1)=0

I always get stuck on the stupidest mistakes.

I really appreciate it! thanks
 

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