System of ODE: derivative inside equation

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Marco Sammito
Marco Sammito 2017-2-24
评论： Torsten 2017-2-24
Hi. I have to solve this system of ODE:
How should I treat x'_3 in the second equation? I tried two different approaches but I get different results:
function equazione()
[t,x] = ode45(@(t,x) F(t,x), [0, 3], [2, 1, 1]);
plot(t,x(:,1))
end
function xp = F(t,x)
xp = zeros(3,1);
xp(1) = x(2);
xp(2) = -t * x(1) - exp(t) * x(2) + 3 * cos(2 * t) + xp(3);% <- See this last term
xp(3) = exp(t);
end
and
function equazione()
[t,x] = ode45(@(t,x) F(t,x), [0, 3], [2, 1, 1]);
plot(t,x(:,1))
end
function xp = F(t,x)
xp = zeros(3,1);
xp(1) = x(2);
xp(2) = -t * x(1) - exp(t) * x(2) + 3 * cos(2 * t) + exp(t);% <- See this last term
xp(3) = exp(t);
end
Red line: 1st approach Blue line: 2nd approach
%
  1 个评论
Torsten
Torsten 2017-2-24
The second approach is the correct one.
In the first approach, you only add 0 to -t * x(1) - exp(t) * x(2) + 3 * cos(2 * t) because xp is preallocated as zeros(3,1). This is obvioulsy incorrect.
Best wishes
Torsten.

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