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> with(DEtools): with(plots):
 

> Lorenz := diff(x(t), t) = sigma*(y(t)-x(t)), diff(y(t), t) = r*x(t)-y(t)-x(t)*z(t), diff(z(t), t) = x(t)*y(t)-b*z(t);
 

Lorenz := diff(x(t), t) = sigma*(y(t)-x(t)), diff(y(t), t) = r*x(t)-y(t)-x(t)*z(t), diff(z(t), t) = x(t)*y(t)-b*z(t)
 

> params := sigma = 10, r = 21, b = 8/3;
 

params := sigma = 10, r = 21, b = 8/3
 

> init1 := x(0) = 4, y(0) = 5, z(0) = 6;
 

init1 := x(0) = 4, y(0) = 5, z(0) = 6
 

> Lorenz1 := [op(subs(params, [Lorenz])), init1];
 

Lorenz1 := [diff(x(t), t) = 10*y(t)-10*x(t), diff(y(t), t) = 21*x(t)-y(t)-x(t)*z(t), diff(z(t), t) = x(t)*y(t)-(8/3)*z(t), x(0) = 4, y(0) = 5, z(0) = 6]
 

> LS1 := dsolve(Lorenz1, numeric):
 

> odeplot(LS1, [x(t), z(t)], 0 .. 30, numpoints = 2400);
 

Plot_2d
 

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