Note that this is the most general form: if there is a coefficient (constant or otherwise) in front of the second derivative, we simply divide the whole equation by that coefficient and redefine the c...Note that this is the most general form: if there is a coefficient (constant or otherwise) in front of the second derivative, we simply divide the whole equation by that coefficient and redefine the coefficients to match Equation \ref{A.36}. Now suppose we have a solution \(y_1 (x)\) of the homogeneous equation (so for the case that \(r (x) = 0\) ).