Getting the particular solution of this differential equation.

[FocusedWolf]

Homework Statement

y''-2y'-3y=-3t*e^(-t)

Homework Equations

Has to be done with method of undetermined coefficients

The Attempt at a Solution

the chacteristic equation is: c1*e^(3t) + c2*e^(-t)

my attempt at Yp is (a*t+b)*e^(-t)... so you that's not it. i tried many versions and i keep on getting a = 3t/4.

the book has the answer as y=c1*e^(3t) + c2*e^(-t)+(3/16)*t*e^(-t)+(3/8)*t^2*e^(-t)

 

[Mindscrape]

Your homogeneous equation has a solution that is of the form of one of your terms in the particular solution. I suggest a similar guess, with a tweak.

 

[HallsofIvy]

Since e^3t is already a solution to the homogeneous equation, you need to multiply your first "guess" by t.

 

[FocusedWolf]

thx i successfully got the answer. At first i tried to get that to work, but then it came to the part where you got to solve for like 3 variables, like a, b, and t... and while glancing over to my calculus book, which has a better writup on differential equation then my differential equation book lol, i saw how you had to deal with this by equating the coeffecients. i don't remember this problem i posted about but it was like you had to separate it where t(a + b) + (a - b) = 3t. and did a + b = 3, and a - b = 0, and solve for a and b that way. it's interesting that that even works cause my ti89 can't do it, which is shocking lol