A certain on-line service claims, "We can find a closed form explicit solution for your ordinary differential equation" (and they supply a price to do so once you submit your ODE to them).
In fact, they claim that "you can find a closed form explicit analytical solution for any ordinary differential equation....a closed form solution expressed in useful functions...."
Of course the claim is manifestly false if they mean in terms of elementary functions. And in the example they provide, they introduce a small perturbation and then provide a solution of the perturbed ODE, not the original one.
What might they mean by their claim?
I didn't want to provide the URL explicitly here, but if you do a web search for
explicit solution for your ordinary differential equation movie clip
then you'll find the web site.