I’ve gotten into Julia to solve a number of ODEs (mostly for boundary value problems) and I’ve started to practice solving them in Julia. I’ve checked a lot of threads and the documentation for Differentialequations.jl but have now been able to find an answer to this problem. In all of the reading I have done, the initial values that we use when defining a problem are always some u(t0) = u0 for a t0 = 0. However, I am encountering a number of ODEs I must solve whose initial conditions are given by some u(t0) = u0 where t0 ≠ 0.
For instance, solving
du/dt + u*tan(t) = exp(2*t)*cos(t), u(0) = 2 looks like
using DifferentialEquations f(u,p,t) = exp(2*t)*cos(t) - u*tan(t) u0 = 2. tspan = (0.,4.) prob = ODEProblem(f,u0,tspan) sol = solve(prob)
However, I am clueless on how to set up
t*du/dt = u + t, u(2) = 8
Thank you so much!