I'm given the differential equation `y'' = -g + a(t)/m`

with `a(t) = k*y'^2`

where `y`

is a function of `t`

(time). My initial conditions are `y(0) = 600;`

and `y'(0) = 0;`

In MATLAB I know how to define `y''`

with

```
ydd = diff(y,t,2) == -g + a(t)/m;
```

but I'm lost at the fact that this is a 'nested' non linear differential equation and I'm not quite sure how to define it, let alone, solve it in MATLAB.

The better first order system is

```
v' = -g + k/m*v^2
y' = v
```

as there is no longer a third unknown function `a(t)`

involved.

Challenge: Solve the first equation manually via separation of variables and partial fraction decomposition or identifying the scaling for the Area tangent hyperbolicus as the integral for the side of `v`

.