Mathematica图形解决方案

Question

我需要帮助解决mathematica的这个数学问题。见附图。 Math Problem Picture Link

Answer 1

从Mathematica Navigator edition 3，第26章微分方程，26.1.3节同步方程，例1，基本技术中获取线索。

vars = {x[t], y[t]};

eqns = {
   x'[t] == x[t] - 2 y[t],
   y'[t] == x[t] - y[t]};

(* define a range of initial conditions *)
range = Flatten[Table[{x0, y0}, {x0, 2, 4}, {y0, 0, 1}], 1];

sols = Function[{x0, y0},
    inits = {x[0] == x0, y[0] == y0};
    vars /. First@DSolve[Join[eqns, inits], vars, t]] @@@ range;

ParametricPlot[sols, {t, 0, 2 Pi},
 PlotLegends -> LineLegend["Expressions",
   LegendLabel -> Placed["Parametric Equations", Above],
   LegendFunction -> Framed]]