# Linear ODE Forms

Linear ODE Forms

The fixed point has many different stability types. A system rarely has an infinite number of solutions along a line in the , plane.

(0,0)

x(t)

y(t)

The fixed point has many different stability types. Only two solutions for fixed points are possible in a linear first-order system: one with an equilibrium point at , or infinitely many solutions along a line in the , plane.

(0,0)

(0,0)

x(t)

y(t)

Red dots represent fixed points or equilibrium points.

Dashed blue lines indicate straight-line solutions.

Dashed black lines indicate nullclines.