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

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L'O.G.
L'O.G. 2023-10-7
评论： Sam Chak 2023-10-9
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.)
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Sam Chak
Sam Chak 2023-10-9
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.

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回答（2 个）

Torsten
Torsten 2023-10-7
移动：Torsten 2023-10-7
If you have two unknown functions (f and g), you need two equations.
Walter Roberson
Walter Roberson 2023-10-8
Ran in:
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

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