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Guess is $y = Ax+B$.

$y''' = 0$

$y' = A$

Thus, the differential equation becomes:

$0 + 8(A) = -8x-3$

Where can I go from here? I can't find an explicit solution for A, and my work doesn't even involve the variable B. Any help?

  • 3
    Well, you started with a *guess* and got stuck. Which kind of suggests that a different guess might be a way out.... Hint: You're going to need at least *some* $x$-term on the left-hand side, so maybe a polynomial with degree $\geq 2$ wouldn't be a bad idea.2012-10-20

1 Answers 1

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You'll need $y_p = (Ax+B)x = Ax^2 + Bx$, since the characteristic eqn. of your ODE has $0$ as a root.

$y'_p = 2Ax + B$

$y'''_p = 0$

So we have:

$0 + 8(2Ax + B) = -8x - 3$

And you should be able to take it from there.