Answer:
See details below
Explanation:
Your equation is
. Solve for the fourth derivative to get

Now apply said change of variables: let
. Then, substituting on out first equation, we obtain the system:



In general, if you have an nth order ordinary differential equation, you can apply the same idea to obtain a system of differential equations with n unknowns. Therefore, solving systems of differential equations is equivalent to solving higher-order differential equations.