# High order differential equations: undetermined coefficients

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1. Dec 6, 2014

### dmoney123

1. The problem statement, all variables and given/known data

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: ?

2. Relevant equations

3. 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)

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

2. Dec 6, 2014

### dwn

Hello dmoney,

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

missed that .... c3e-t

3. Dec 6, 2014

### SteamKing

Staff Emeritus
Your characteristic equation is third order in r. How many roots are there?

4. Dec 6, 2014

### dmoney123

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