Hello, I have solved a system of ODE equation by using Jacobian Sparsity method. I am reading this link ODE Problems · DifferentialEquations.jl. It says that we can find df/du by using the command `jac(J,u,p,t)`

or `J=jac(u,p,t)`

. But, I have no idea how to use it. Where to write this command in the code to get df/du. Kindly let me know. I am writing it in a new line. But, it is giving error that “jac is not defined”.

My code is like:

using DifferentialEquations

# Define your ODE equation

function my_ode(du,u,p,t)

du[1] = u[2]

du[2] = -u[1] - 0.1*u[2]

end

# Define the initial conditions and time span

u0 = [1.0, 0.0]

tspan = (0.0, 10.0)

p = 0

using Symbolics

du0 = copy(u0)

jac_sparsity = Symbolics.jacobian_sparsity((du,u)->my_ode(du,u,p,0.0),du0,u0)

f = ODEFunction(my_ode;jac_prototype=float.(jac_sparsity))

prob_sparse = ODEProblem(f,u0,tspan,p)

alg = Tsit5()

sol = solve(prob_sparse,alg)

answer = jac(J,u,p,t)

print(answer)

Here I used very simple ODE, but actual ODE that I am solving is very complex and its jacobian and direcational derivatives cannot found easity. So, I need to find it by using jac command.