Question

What is the solution to y''(t) -2y'(t) - 3y(t) = 3e^2t

Answer 1

\[y(t) = c_1 e^{-t}+c_2 e^{3 t}-e^{2 t}+2 e^2/3\]

Answer 2

Thats the sol. from w.a. Its been awhile since I did diffs. There's a bunch of little tricks and techniques for solving different forms of differential equations. If you want to know how to do it let me know. Id probably have to grab my diffs book.

Answer 3

auxiliary eq. is D^2-2D-3=0
D^2-3D+1D-3=0
D(D-3)+1(D-3)=0
(D-3)(D+1)=0
D=3,-1
\[complementary solution =c1e ^{3t}+c2e ^{-t}\]
to find P.I
let \[y=A ^{2t},y'=2Ae ^{2t },y \prime \prime=4Ae ^{2t}\]
put in differential eq.
\[4Ae ^{2t}-2*2Ae ^{2t}-3Ae ^{2t}=3e ^{2t}\]
-3A=3,
A=-1
c.s is\[y=c1e ^{3t}+c2e ^{-t}-e ^{2t}\]

Answer 4

correction
to find p.I
[\let y=Ae ^{2t}\]