Differential Equation, nonhomogeneous equation

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Homework Statement



Find the general solution:
y'' - y' - 2y = -2t + 4t^2


Homework Equations





The Attempt at a Solution



r_1 = 2, r_2 = (-1)

Set Y(t) = At^2 + B^t + C
Y' = 2At + B
Y'' = 2A

2A - 2At + B - 2At^2 + Bt + C = -2t + 4t^2

-2At^2 + (B-2A)t + 2A + B + C = -2t + 4t^2

-2A = 4
B - 2A = (-2)
2A + B + C = 0

The solution should have -2 = A, 3 = B, and -7/2 = C.
But when I solve it, given the equations above, I don't get that. I only have A right.

What's wrong?

Thank you
 

Answers and Replies

  • #2
BruceW
Homework Helper
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Set Y(t) = At^2 + B^t + C
Y' = 2At + B
Y'' = 2A

2A - 2At + B - 2At^2 + Bt + C = -2t + 4t^2
The method is right, but there are several mistakes when you substitute into the equation. Maybe do this in a couple of steps, instead of one.
 
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Thanks
 

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