Consider the differential equation dx/dt4x^4-x^2 Find the critical points, equil
ID: 3004347 • Letter: C
Question
Consider the differential equation dx/dt4x^4-x^2 Find the critical points, equilibrium solutions and draw the phase diagram for the equation above. Classify each critical point/equilibrium as either stable, unstable, or semi-stable. Using a computer program, plot the slope field (direction field). Plot all the equilibrium solutions, plot a solution above the highest equilibrium, plot a solutions below the lowest equilibrium, and at least on solution between each of the equilibrium.To plot the slope field an solutions you may wish to use MAPLE or the MATLAB script airfield.Explanation / Answer
1. critical point- rhs=0, x=0 , 1/2, -1/2
differentaite once again and see the sign of second derivative at critical points. sign will determine stability.
if sign negative- stable(-1/2), sign is positive then unstable(1/2) , if 0 then semi stable(0)
2. matlab/maple needed