IVP with singularity

The equation \(u'=(u+t)^2\) gives us some trouble.

using FundamentalsNumericalComputation
f = (u,p,t) -> (t+u)^2

ivp = ODEProblem(f,1.,(0.,1.))
sol = solve(ivp,Tsit5());
┌ Warning: dt <= dtmin. Aborting. There is either an error in your model specification or the true solution is unstable.
└ @ DiffEqBase /Users/driscoll/.julia/packages/DiffEqBase/Xoaan/src/integrator_interface.jl:343

The warning message we received can mean that there is a bug in the formulation of the problem. But if everything has been done correctly, it suggests that the solution may not exist past the indicated time. This is always a possibility in nonlinear ODEs.

plot(sol, label="", yaxis=(:log10,"u(t)"), title="Finite-time blowup")