Originally Posted by

**CaptainBlack** Clearly if x is ever negative the derivative is negative, and gets more

negative the more negative x becomes, so there is run away growth

in the absolute value of x, and the growth is in the direction of increasingly

more negative x. So as time goes to infty x goes to -infty.

If x is ever positive but <50 dx/dt is positive so x is growing, but it must

level off where dx/dt=0, which is at x=50. So if x starts with a value in

the interval (0,50) it grows closer and closer to 50, so as t->infty

x->infty.

If x is ever positive but >50 dx/dt is negative so x is declining, but it must

level off where dx/dt=0, which is at x=50. So if x starts with a value in

the >50 it grows closer and closer to 50, so as t->infty

x->infty.

If x(0)=50, then dx/dt=0, so x remains at a value of 50. However any small

disturbance away from x=50 will decay back towards x=50, so x=50 is a

stable equilibrium.

If x(0)=0, then dx/dt=0, so x remains at a value of 0. However any small

disturbance away from x=0 will grow away from x=0, so x=0 is an

unstable equilibrium.

RonL