May someone please help me on the procedures to solve these differential equations

I tried solving it using MATLAB ode45 but all the information and examples I can find are on simple second order equations, these ones are more complicated so I need a simple explanation on the steps I should follow in order to get the solution.
 
I tried solving it using MATLAB ode45 but all the information and examples I can find are on simple second order equations, these ones are more complicated so I need a simple explanation on the steps I should follow in order to get the solution.
If I were to solve this problem, I would start with:

\(\displaystyle u \ = \frac{dx}{dt}\) ..... and ..... \(\displaystyle v \ = \frac{dy}{dt}\) then

\(\displaystyle \frac{du}{dt} \ = \frac{d^2x}{dt^2}\) ..... and ..... \(\displaystyle \frac{dv}{dt} \ = \frac{d^2y}{dt^2}\)

and continue....

Please share your work/thoughts
 
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