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can you please help me solve this diffetential equation system?

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SOUGLES STAMATIS
SOUGLES STAMATIS on 7 Apr 2021
Commented: Alan Stevens on 8 Apr 2021
I need to solve a differential system and I coded in this way . I doesn't seem to work. I want to solve it only for t [0,4]. how can i do that?
syms x1(t) x2(t) x3(t) x4(t) x5(t) x6(t)
b=4.2030*10^5
m=1.0508*10^6
k=3.5025*10^9
A = [-2*b/(3*m) b/(3*m) 0 1/(3*m) -1/(3*m) 0 ;
b/(2*m) -2*b/(2*m) b/(2*m) 0 1/(3*m) -1/(3*m) ;
0 b/m -b/m 0 0 1/m ;
-k 0 0 0 0 0 ;
k -k 0 0 0 0 ;
0 k -k 0 0 0];
B = [-b/(3*m)*(1.8747*log(t)+8.6905);
0;
0;
-k*(1.8747*log(t)+8.6905);
0;
0;];
Y = [x1; x2; x3; x4; x5; x6];
odes = diff(Y) == A*Y + B
C = Y(0) == [0;0;0;0;0;0];
[x1Sol(t), x2Sol(t), x3Sol(t), x4Sol(t), x5Sol(t), x6Sol(t)] = dsolve(odes,C);
x1Sol(t) = simplify(x1Sol(t))
x2Sol(t) = simplify(x2Sol(t))
x3Sol(t) = simplify(x3Sol(t))
x4Sol(t) = simplify(x4Sol(t))
x5Sol(t) = simplify(x5Sol(t))
x6Sol(t) = simplify(x6Sol(t))

Answers (1)

Alan Stevens
Alan Stevens on 7 Apr 2021
You have log(t) in the definition of B. This causes problems at t = 0.
  2 Comments
Alan Stevens
Alan Stevens on 8 Apr 2021
Like this
x0 = [0;0;0;0;0;0];
tspan = [0.01 4];
[t, x] = ode45(@bc, tspan, x0);
plot(t,x),grid
function xdot = bc(t,x)
b=4.2030*10^5;
m=1.0508*10^6;
k=3.5025*10^9;
A = [-2*b/(3*m) b/(3*m) 0 1/(3*m) -1/(3*m) 0 ;
b/(2*m) -2*b/(2*m) b/(2*m) 0 1/(3*m) -1/(3*m) ;
0 b/m -b/m 0 0 1/m ;
-k 0 0 0 0 0 ;
k -k 0 0 0 0 ;
0 k -k 0 0 0];
B = [-b/(3*m)*(1.8747*log(t)+8.6905);
0;
0;
-k*(1.8747*log(t)+8.6905);
0;
0;];
xdot = A*x + B;
end
You might need to plot the different x's on separate graphs to see them all properly.
Note that the results will be somewhat different depending on your starting value for t.

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