- #1
- 5
- 0
Homework Statement
Find the solution to :y''+2y'+y=t
Homework Equations
Suppose y(t)=B1t2+B2t+B3
And I believe, Y(t)=Yh+Yp. That is the solution is equal to the solution to the homogenous equation, plus the particular solution.
The Attempt at a Solution
First Solve the homogeneous equation:
y(t)=B1t2+B2t+B3
y'(t)=2B1t+B2
y''(t)=2B1
Substitute this back into the homogenous problem(y''+2y'+y=0) gives:
2B1+2(2B1t+B2)+B1t2+B2t+B3=0
Rearrange:
B1(t2+4t+2) +B2(t+2)+B3=0
Solution is t=-2 or B1,B2,B3=0
Now I'm unsure of what to do?
As for the particular solution say Yp:
Yp=ct, where c is a constant so,
Y'p=c
Y''p=0
Substitute this into :y''+2y'+y=t
0+2c+ct=t
c=?
Thanks for any help.