Uppgift 6.2: 32 

restart; -1; with(LinearAlgebra); -1; with(DEtools); -1 

`:=`(f[1], `+`(`*`(x, `*`(y)), `-`(2))); -1; `:=`(f[2], `+`(x, `-`(`*`(2, `*`(y))))); -1 

`:=`(jmv, solve({f[1], f[2]})) 

{y = 1, x = 2}, {y = -1, x = -2} (3.1)
 

`:=`(df, Matrix(%id = 21954888)) 

Matrix(%id = 3677604) (3.2)
 

`:=`(P[1], map(eval, df, jmv[1])) 

Matrix(%id = 7697356) (3.3)
 

Eigenvalues(P[1]) 

Vector[column](%id = 21782276) (3.4)
 

evalf(%) 

Vector[column](%id = 6708908) (3.5)
 

Labil jämviktspunkt. 

`:=`(P[2], map(eval, df, jmv[2])) 

Matrix(%id = 22232144) (3.6)
 

Eigenvalues(P[2]) 

Vector[column](%id = 7773712) (3.7)
 

Asymptotiskt stabil jämviktspunkt av spiraltyp. 

Kontroll!! 

`:=`(ode, [(D(x))(t) = eval(f[1], [x = x(t), y = y(t)]), (D(y))(t) = eval(f[2], [x = x(t), y = y(t)])]); -1 

DEplot(ode, [x(t), y(t)], t = 0 .. 25, x = -3 .. 3, y = -2 .. 2, [[x(0) = 1.5, y(0) = 2], [x(0) = 2, y(0) = -2]], linecolor = [BLUE, BLACK], arrows = MEDIUM, stepsize = 0.2e-1)
DEplot(ode, [x(t), y(t)], t = 0 .. 25, x = -3 .. 3, y = -2 .. 2, [[x(0) = 1.5, y(0) = 2], [x(0) = 2, y(0) = -2]], linecolor = [BLUE, BLACK], arrows = MEDIUM, stepsize = 0.2e-1) 

Plot_2d