Riktningsfält 

Exempel 1. 

restart 

with(DEtools); -1 

`:=`(ode, diff(y(x), x) = `+`(`-`(`*`(r, `*`(`+`(1, `-`(`/`(`*`(y(x)), `*`(T)))), `*`(`+`(1, `-`(`/`(`*`(y(x)), `*`(K)))))))))) 

diff(y(x), x) = `+`(`-`(`*`(r, `*`(`+`(1, `-`(`/`(`*`(y(x)), `*`(T)))), `*`(`+`(1, `-`(`/`(`*`(y(x)), `*`(K))))))))) (5.1)
 

`:=`(ode1, eval(ode, {K = 10, T = 5, r = 1})) 

diff(y(x), x) = `+`(`-`(`*`(`+`(1, `-`(`*`(`/`(1, 5), `*`(y(x))))), `*`(`+`(1, `-`(`*`(`/`(1, 10), `*`(y(x))))))))) (5.2)
 

DEplot(ode1, y(x), x = 0 .. 50, y = -2 .. 15, arrows = MEDIUM) 

Plot_2d
 

DEplot(ode1, y(x), x = 0 .. 50, y = -2 .. 15, [[y(0) = 5.5], [y(0) = 4.5], [y(0) = 14]], arrows = MEDIUM, linecolour = [RED, GREEN, BLUE]); 1
DEplot(ode1, y(x), x = 0 .. 50, y = -2 .. 15, [[y(0) = 5.5], [y(0) = 4.5], [y(0) = 14]], arrows = MEDIUM, linecolour = [RED, GREEN, BLUE]); 1
 

Plot_2d
 

Exempel 2. 

restart; -1; with(DEtools); -1 

`:=`(ode, diff(y(x), x) = `/`(`*`(`^`(x, 2)), `*`(`+`(1, `-`(`*`(`^`(y(x), 2))))))) 

diff(y(x), x) = `/`(`*`(`^`(x, 2)), `*`(`+`(1, `-`(`*`(`^`(y(x), 2)))))) (5.3)
 

DEplot(ode, y(x), x = -3 .. 3, y = -3 .. 3, arrows = MEDIUM) 

Plot_2d
 

DEplot(ode, y(x), x = -3 .. 3, y = -3 .. 3, [[y(1) = -2], [y(1) = 2]], arrows = MEDIUM, linecolour = [BLUE, GREEN], stepsize = 0.1e-2); 1
DEplot(ode, y(x), x = -3 .. 3, y = -3 .. 3, [[y(1) = -2], [y(1) = 2]], arrows = MEDIUM, linecolour = [BLUE, GREEN], stepsize = 0.1e-2); 1
 

 

Warning, plot may be incomplete, the following errors(s) were issued:
 

  cannot evaluate the solution further left of -1.4422499, probably a singularity
 

Warning, plot may be incomplete, the following errors(s) were issued:
  cannot evaluate the solution further right of 1.7099760, probably a singularity
Plot_2d
 

dsolve(ode, y(x)) 

y(x) = `+`(`*`(`/`(1, 2), `*`(`^`(`+`(`-`(`*`(4, `*`(`^`(x, 3)))), `-`(`*`(12, `*`(_C1))), `*`(4, `*`(`^`(`+`(`-`(4), `*`(`^`(x, 6)), `*`(6, `*`(`^`(x, 3), `*`(_C1))), `*`(9, `*`(`^`(_C1, 2)))), `/`(1...
y(x) = `+`(`*`(`/`(1, 2), `*`(`^`(`+`(`-`(`*`(4, `*`(`^`(x, 3)))), `-`(`*`(12, `*`(_C1))), `*`(4, `*`(`^`(`+`(`-`(4), `*`(`^`(x, 6)), `*`(6, `*`(`^`(x, 3), `*`(_C1))), `*`(9, `*`(`^`(_C1, 2)))), `/`(1...
y(x) = `+`(`*`(`/`(1, 2), `*`(`^`(`+`(`-`(`*`(4, `*`(`^`(x, 3)))), `-`(`*`(12, `*`(_C1))), `*`(4, `*`(`^`(`+`(`-`(4), `*`(`^`(x, 6)), `*`(6, `*`(`^`(x, 3), `*`(_C1))), `*`(9, `*`(`^`(_C1, 2)))), `/`(1...
y(x) = `+`(`*`(`/`(1, 2), `*`(`^`(`+`(`-`(`*`(4, `*`(`^`(x, 3)))), `-`(`*`(12, `*`(_C1))), `*`(4, `*`(`^`(`+`(`-`(4), `*`(`^`(x, 6)), `*`(6, `*`(`^`(x, 3), `*`(_C1))), `*`(9, `*`(`^`(_C1, 2)))), `/`(1...
y(x) = `+`(`*`(`/`(1, 2), `*`(`^`(`+`(`-`(`*`(4, `*`(`^`(x, 3)))), `-`(`*`(12, `*`(_C1))), `*`(4, `*`(`^`(`+`(`-`(4), `*`(`^`(x, 6)), `*`(6, `*`(`^`(x, 3), `*`(_C1))), `*`(9, `*`(`^`(_C1, 2)))), `/`(1...
y(x) = `+`(`*`(`/`(1, 2), `*`(`^`(`+`(`-`(`*`(4, `*`(`^`(x, 3)))), `-`(`*`(12, `*`(_C1))), `*`(4, `*`(`^`(`+`(`-`(4), `*`(`^`(x, 6)), `*`(6, `*`(`^`(x, 3), `*`(_C1))), `*`(9, `*`(`^`(_C1, 2)))), `/`(1...
y(x) = `+`(`*`(`/`(1, 2), `*`(`^`(`+`(`-`(`*`(4, `*`(`^`(x, 3)))), `-`(`*`(12, `*`(_C1))), `*`(4, `*`(`^`(`+`(`-`(4), `*`(`^`(x, 6)), `*`(6, `*`(`^`(x, 3), `*`(_C1))), `*`(9, `*`(`^`(_C1, 2)))), `/`(1...
y(x) = `+`(`*`(`/`(1, 2), `*`(`^`(`+`(`-`(`*`(4, `*`(`^`(x, 3)))), `-`(`*`(12, `*`(_C1))), `*`(4, `*`(`^`(`+`(`-`(4), `*`(`^`(x, 6)), `*`(6, `*`(`^`(x, 3), `*`(_C1))), `*`(9, `*`(`^`(_C1, 2)))), `/`(1...
y(x) = `+`(`*`(`/`(1, 2), `*`(`^`(`+`(`-`(`*`(4, `*`(`^`(x, 3)))), `-`(`*`(12, `*`(_C1))), `*`(4, `*`(`^`(`+`(`-`(4), `*`(`^`(x, 6)), `*`(6, `*`(`^`(x, 3), `*`(_C1))), `*`(9, `*`(`^`(_C1, 2)))), `/`(1...
y(x) = `+`(`*`(`/`(1, 2), `*`(`^`(`+`(`-`(`*`(4, `*`(`^`(x, 3)))), `-`(`*`(12, `*`(_C1))), `*`(4, `*`(`^`(`+`(`-`(4), `*`(`^`(x, 6)), `*`(6, `*`(`^`(x, 3), `*`(_C1))), `*`(9, `*`(`^`(_C1, 2)))), `/`(1...
(5.4)
 

dsolve(ode, y(x), implicit) 

`+`(`*`(`/`(1, 3), `*`(`^`(x, 3))), `-`(y(x)), `*`(`/`(1, 3), `*`(`^`(y(x), 3))), _C1) = 0 (5.5)