How do i solve differential equation 2nd oder simbolically and numerically?

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Karl-JR
Karl-JR 2023-1-4
评论： Karl-JR 2023-1-4
Hello everyone i am completly new to Matlab and I have a problem with an exercise in my practice book. I have this differential equation:
y(0) = 1
and i want to solve it simbolically and numerically in matlab.
so first i have to change it in first order differential equation:
But how do i continue? I´m trying for hours at this point😅

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Torsten
Torsten 2023-1-4
编辑：Torsten 2023-1-4
Ran in:
syms t y(t) sigma(t)
eqn_diff = diff(y,t,2)+3*diff(y,t)+y(t)-2*sigma(t)==0;
ysol(t) = dsolve(eqn_diff);
var = symvar(ysol)
var = 
eqn_alg = subs(ysol,var(1),0)-1==0
eqn_alg(t) = 
C1 = solve(eqn_alg,var(2));
ysol = subs(ysol,var(2),C1)
ysol(t) = 
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Torsten
Torsten 2023-1-4
编辑：Torsten 2023-1-4
You specified one initial condition for a second-order ODE (y(0)=1). So one free parameter (in this case C1) can be eliminated from the two degrees of freedom (C1 and C2) for y. If you impose a second condition on y, you can get a unique solution (means: you can also eliminate C2).

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