One of the most celebrated set of differential equations in physics are the Lorenz equations:

$=(),=,=,$

where $,$ r and b are constants $($named such for historical reasons$).$

The reason for their fame is that they were one of the first examples of deterministic chaos.

Task: solve the Lorenz equations for the case $=10,=28\mathrm{.}5$ and $=10/3$ in the range from $=0$ to $=40,$ with initial conditions $(,,)=(0,1,0).$ Set the number of evaluation points in time to $10000.$ Create a function called butterfly$()$ which encapsulates the full solution code and returns the result of solve$\_$ivp$()$ such that it can be called in the tests, without input arguments $($see tests$).$

Plot the variable z against x$,$ a trajectory plot. You should see a picture of the famous strange attractor of the Lorenz equations, a lop$-$sided butterfly shaped plot that never repeats itself. The plot should not be part of the butterfly$()$ function.