Improvements based on review (#328)

* README: more explanation for related-package trade-offs

* Update and correct second-order-ODE docs

* Update the related-package section in `docs/src/index.md`

Author: nathanaelbosch

README.md

@@ -77,5 +77,5 @@ This includes not just bugs and feature requests but also general questions abou
 
 ## Related packages
 
-- [probdiffeq](https://pnkraemer.github.io/probdiffeq/): Fast and feature-rich filtering-based probabilistic ODE solvers in JAX.
-- [ProbNum](https://probnum.readthedocs.io/en/latest/): Probabilistic numerics in Python. It has not only probabilistic ODE solvers, but also probabilistic linear solvers, Bayesian quadrature, and many filtering and smoothing implementations.
+- [ProbDiffEq](https://pnkraemer.github.io/probdiffeq/) is similar in scope to ProbNumDiffEq.jl and it provides fast and feature-rich probabilistic ODE solvers but is implemented in Python and built on JAX.
+- [ProbNum](https://probnum.readthedocs.io/en/latest/) implements a wide range of probabilistic numerical methods, not only for ODEs but also for linear algebra, quadrature, and filtering/smoothing. It is implemented in Python and NumPy, and it focuses more on breadth and didactic purposes than on performance.

docs/src/index.md

@@ -40,5 +40,5 @@ For a quick introduction check out the "[Solving ODEs with Probabilistic Numeric
 
 ## Related packages
 
-- [probdiffeq](https://pnkraemer.github.io/probdiffeq/): Fast and feature-rich filtering-based probabilistic ODE solvers in JAX.
-- [ProbNum](https://probnum.readthedocs.io/en/latest/): Probabilistic numerics in Python. It has not only probabilistic ODE solvers, but also probabilistic linear solvers, Bayesian quadrature, and many filtering and smoothing implementations.
+- [ProbDiffEq](https://pnkraemer.github.io/probdiffeq/) is similar in scope to ProbNumDiffEq.jl and it provides fast and feature-rich probabilistic ODE solvers but is implemented in Python and built on JAX.
+- [ProbNum](https://probnum.readthedocs.io/en/latest/) implements a wide range of probabilistic numerical methods, not only for ODEs but also for linear algebra, quadrature, and filtering/smoothing. It is implemented in Python and NumPy, and it focuses more on breadth and didactic purposes than on performance.

docs/src/tutorials/dynamical_odes.md

@@ -92,10 +92,10 @@ As a result, we can use the `EK1` both for first and second order ODEs, but it a
 julia> using BenchmarkTools
 
 julia> @btime solve(prob, EK1(order=3), adaptive=false, dt=1e-2);
-  766.312 ms (400362 allocations: 173.38 MiB)
+  317.336 ms (140561 allocations: 140.41 MiB)
 
-julia> @btime solve(prob2, EK1(order=4), adaptive=false, dt=1e-2);
-  388.301 ms (510676 allocations: 102.78 MiB)
+julia> @btime solve(prob2, EK1(order=3), adaptive=false, dt=1e-2);
+  136.654 ms (180647 allocations: 47.95 MiB)
 ```
 
 ## Energy preservation