High order differential equations: undetermined coefficients

[dmoney123]

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^tRHS

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 don't think it does.Thanks

 

[dwn]

Hello dmoney,

Your LHS should be y_c(t) = c₁e^t + c₂e^(0*t) = c₁e^t + c₂

missed that ... c₃e^-t

 

[SteamKing]

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

 

[dmoney123]

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