# A particular solution to the differential equation y'' + 2y' + y = t^2 + 3?

1. Oct 6, 2012

### the_Doctor111

A particular solution to the differential equation y'' + 2y' + y = t^2 + 3?
is t^2 - 4t +7 in the answers, but i get t^2 - 4t + 9 so where am i going wrong.....

y = Ay^2 + by + c
y' = 2Ay + B
y'' = 2A

2A + 2(2Ay + B) + Ay^2 +By + c = t^2 + 3
A(y^2) + (4A+B)y +(2A +2B+c) = t^2 + 0t + 3

A = 1

B + 4A = 0 → b = -4

C + 2B + 2A = 3 → b = 9

Sorry if it's just an arithmetical error i'm pretty tired

2. Oct 6, 2012

### SammyS

Staff Emeritus
Shouldn't those be t's & not y' in:

y = At2 + Bt + C

y' = 2At + B

y'' = 2A

I also get:
C + 2B + 2A = 3  →  C = 3 -2B -2A  →  C = 3 - 2(-4) - 2(1) = 9

Did you copy the problem wrong?

3. Oct 6, 2012

### the_Doctor111

I did copy it right the answers must just be wrong

4. Oct 6, 2012

### LCKurtz

You could plug your $y_p$ in and see if it works. That would settle it.