Trying to solve a second order differential equation. Your advices

Specific Domains Optimization (Mathematical)
2

No, you’re missing a ./R on the second term. This should be it:

using OrdinaryDiffEq, Plots

#Parameters
P = 75.0            #pression 50 => collapse

#initial conditions
R₀ = [5.0]
dR₀ = [1.0]
tspan = (0.0,50.0)

#numerical
function rp(ddR, dR, R, P, t)
     @. ddR = (P - (1.5 *dR^2))/R
end

#pass to the solver
probleme = SecondOrderODEProblem(rp, dR₀, R₀, tspan, P)
solution = solve(probleme, DPRKN6())

@show solution.t
@show solution.u

#graph
plot(solution, vars=(2), linewidth=2,
        xaxis = "t ", yaxis = "R",
        framestyle = :box)

savefig("RP1.pdf")

Fixing that term seems to stabilize the solution a lot more too, so I don’t think a method for stiff equations is necessary.