To solve for $x$ in the general solution of the differential equation, we need more context—specifically, initial conditions or boundary conditions. Since none are provided in the image or your request, we'll consider the solution we derived:

$y(x) = C_1 \cos(x) + C_2 \sin(x) - \frac{1}{3} \cos(2x)$

Case 1: General Form

If there are no initial or boundary conditions, then $x$ is simply the variable of the function $y(x)$, and there is no specific value for $x$ unless conditions are provided.

Case 2: With Specific Initial or Boundary Conditions

If you are given initial conditions such as $y(0) = y_0$ and $y'(0) = y'_0$, you could determine the constants $C_1$ and $C_2$, and then you might be able to solve for $x$ when $y(x) = 0$ or another specific value.

If you have specific conditions or additional details on the problem, please share them so we can solve for $x$ under those conditions.

Do you have initial conditions or more specific criteria for $x$?