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?
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?
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.