1. Sketch the nullclines in the xy phase plane, identify steady states, find the linearized system at each steady state and determine stability of each steady state. (a) dx = y -x, dt dy = x-1. dt

Graph the phase portrait of the system..

Let U(x) = 3x² - 4x be a potential energy in one dimension. Find and classify the equilibria of the system. 3 If one equlibrium is stable and the other unstable, enter the stable equilibrium first. If both equilibria have the same stability, enter them in either order. x= Stable O Unstable O Stable Unstable 41

Choose one an unstable equilibrium solution. an asymptotically stable equilibrium solution. no equilibrium solution at all. a semistable equilibrium solution.

2a. Find a change of variable that transforms the equation into an autonomous equation change of variable: new equation: b. Sketch the phase line for the resulting equation and use it to sketch graphs of the long-term behaviors of all the qualitatively different solutions for the new variable, and then for the original equation.

3 please