Is the C in the numerator the same thing as the c in the denominator? The partial derivative of C with respect to X, compared to the +c^2*omega^2, or is it C^2 * omega^2 ?
Is the x on the left hand side, x(t), the same thing as the x that is being used as the partial delta C / delta x ? If so then you are attempting to take the partial derivative with respect to a function and that brings in the Calculus of Variations, a more difficult situation.
