How to split initial conditions across multiple timesteps

General Usage
1

I have a differential equation ddf = f/x^2 - df/x - k*f^2/x and I’d know f(0) = 0 and df(1) = 1. How can I tell DifferentialEquations.jl about those initial conditions?

2

I think you want a boundary value problem, but that first condition looks problematic since ddf is undefined at x=0. Here is an example solved on (1.0, 2.0) with f(1)=0 and df(2)=1:

using DifferentialEquations

function f!(du, u, p, t)
    du[1] = u[2]
    du[2] = u[1]/t^2 - u[2]/t - p*u[1]^2/t
    nothing
end

function bc!(residual, u, p, t)
    residual[1] = u[1][1] # f(start of tspan) = 0
    residual[2] = u[end][2] - 1 # df(end of tspan) = 1
    nothing
end

bvp = BVProblem(f!, bc!, [0.0, 0.0], (1.0, 2.0), 1.0)

sol = solve(bvp, GeneralMIRK4(), dt=0.05)