![(*3.9*)σ = 10. ; ρ = 28. ; β = 2.6667 ; DSolve[{x '[t] ᡫ ... 0, 10}] ParametricPlot3D[{x[t], y[t], z[t]}/.%[[1]], {t, 0, 10}, PlotPoints300]](../HTMLFiles/ex05_solutions_62.gif)
Solutions
Solving a set of differential equations with DSolve is just as easy as solving a set of ordinary equations with Solve. Here, again, DSolve fails, and NDSolve is needed. Note that the number of required initial conditions is 3, which is the order of this set of equations. Note also that {x(0)=0, y(0)=0,z(0)=0} is not a good set of initial conditions, because these force the derivatives to zero and the graph reduces to a point.
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![DSolve[{x^′[t] 10. x[t] (-x[t] + y[t]), y^′[t] 28. x[t] - y[t] - x[t] z[t], z^′[t] x[t] y[t] - 2.6667 z[t]}, {x[t], y[t], z[t]}, t]](../HTMLFiles/ex05_solutions_63.gif){kind=small}
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![{{x[t] InterpolatingFunction[{{0., 10.}}, <>][t], y[t] InterpolatingFunction[{{0., 10.}}, <>][t], z[t] InterpolatingFunction[{{0., 10.}}, <>][t]}}](../HTMLFiles/ex05_solutions_64.gif){kind=small}
![[Graphics:../HTMLFiles/ex05_solutions_65.gif]](../HTMLFiles/ex05_solutions_65.gif)
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| Created by Mathematica (April 10, 2007) |  |