How do you set up an ode solver with a more than one function in the ode?

For example, if you have an ode such as a*df(t)/dt + b*dg(t)/dt + f(t) + g(t) + c = 0 that you'd like to solve and if you want to set one of the derivatives to be zero, how do you do that?

(By "ode solver" in the title I mean solve numerically.)

[Sam Chak]

Hi @L'O.G.

Please correct me if I'm wrong. In your update, you mentioned that you want to numerically solve the ODE of this form:

I'm not so sure, but this form looks like the first-order "Exact differential equation," and I don't remember how to solve it on pen and paper. Suppose that , and . If and , then the equation is balanced:

.

[L'O.G.]

@Sam Chak Thanks, it is of that form, but this isn't necessarily going to be something that cancels. How do you solve this numerically using one of the ode solvers?

[Walter Roberson]

Use ode15i

[Sam Chak]

Hi @L'O.G.

I would like to suggest providing a specific example of this generic "Exact differential equation" form:

This would allow us to test which ODE solver might be suitable for solving it.

Answer 1

[Torsten]

If you have two unknown functions (f and g), you need two equations.

Answer 2

[Walter Roberson]

syms f(t) g(t) a b c
df = diff(f);
dg = diff(g);
eqn = a*df + b*dg + f(t) + g(t) + c == 0

eqn(t) = 

sol = dsolve(eqn, g)

sol = struct with fields:
    g: 0
    f: exp(-t/a)*(C1 - c*exp(t/a))

eqn2 = subs(diff(sol.f), t, 0) == 0

eqn2 = 

constant_of_integration = setdiff( symvar(eqn2), [a b c])

constant_of_integration = 

solution_for_constant = solve(eqn2, constant_of_integration)

solution_for_constant = 

0

subs(subs(eqn, sol), constant_of_integration, solution_for_constant)

ans(t) = 

subs(sol,  constant_of_integration, solution_for_constant)

ans = struct with fields:
    g: 0
    f: -c