Encuentre soluciones simbólicas para ecuaciones diferenciales de retardo

Resuelva una ecuación de retardo de primer orden usando DSolve.

 In[1]:= Xsol = DSolve[{x'[t] == x[t - 1]^2, x[t /; t < 0] == a t}, x[t], {t, 0, 2}]
 Out[1]=
 In[2]:= XPlot[Evaluate[Table[x[t] /. sol[[1]], {a, 1, 5}]], {t, -1, 2}, Exclusions -> None]
 Out[2]=

Resuelva una ecuación de retardo de quinto orden.

 In[3]:= Xsol = DSolve[{x'''''[t] == -x[t - 2], x[t /; t <= 0] == a t}, x, {t, 0, 10}];
 In[4]:= XPlot[Evaluate[Table[x[t] /. sol[[1]], {a, 1, 4, 1/3}], {t, -1, 10}], WorkingPrecision -> 400, PlotRange -> All, Exclusions -> None]
 Out[4]=

Resuelva un sistema de ecuaciones de retardo.

 In[5]:= Xeqns = {x'[t] == a y[t - 1] + y[t - 3], y'[t] == x[t - 1], x[t /; t <= 0] == t, y[t /; t <= 0] == t^2};
 In[6]:= Xsol = DSolve[eqns, {x, y}, {t, 0, 5}];
 In[7]:= XParametricPlot[ Evaluate[Table[{x[t], y[t]} /. sol, {a, -1, 2, 1/3}]], {t, 0, 5}, WorkingPrecision -> 200, Exclusions -> None]
 Out[7]=

Mathematica

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