Dear all, I have to study the solution of a retarded ODE
x'(t)=ax(t)+bx(t-t_0)
for t>t_0
The initial data x0:[0,t0]-->R is a function defined in the following way x0(t)=f1(t), for 0<t<t' x0(t)=f2(t), for t'<t<t_0.
My code is the following:
Alpha = Pi/4
solu = NDSolve[ {r'[\[Theta]] ==
r[\[Theta]] Cot[\[Pi]/3] - r[\[Theta] - 7/3 \[Pi]]/ Sin[\[Pi]/3],
r[\[Theta] /; 0 <= \[Theta] <= Alpha] ==
1/(Cos[Alpha]*Sin[Pi/3 + Alpha - \[Theta]]),
r[\[Theta] /;
Alpha < \[Theta] <= 2 Pi] == (Tan[Alpha]*Cot[Pi/3] + 1)*
Exp[(\[Theta] - Alpha)*Cot[Pi/3]],
r[\[Theta] /;
2 Pi < \[Theta] <=
2 Pi + Alpha + Pi/3] == ((Tan[Alpha]*Cot[Pi/3] + 1)*
Exp[(2 Pi - Alpha)*Cot[Pi/3]] - 1/Cos[Alpha])*
Exp[Cot[Pi/3]*\[Theta]]}, r, {\[Theta], 0, 4 \[Pi]}]
Plot[Evaluate[{ r[\[Theta]]} /. solu], {\[Theta], 0, 4 \[Pi]}]
The program does not recognize my commands, how can I modify the input of the initial data? Thanks
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