# Sketch for differential equation

Determine all resting positions for differential equation $x'=f(x,\mu)$. Examine whether the resting positions are attractive or repulsive.

$x'=x^2-\mu$

Make a sketch in the plane $(\mu,x)$ where the corresponding resting positions are drawn on vertical lines $\mu=const$ and the behavior of the solutions for the respective value are shown with arrays.

Note: Branching diagram.

Solution:

$x=+-\sqrt(\mu)$

$f(x)=x^2-\mu$

$f'(x)=2x$

$f(-\mu)=-2\sqrt\mu$ attractive

$f(\mu)=2\sqrt\mu$ repulsive.

But how do I make sketch?