Homework will be due Wednesdays, in class.
Click the item to unroll the problem list.
Sunday, noon  updated. Tuesday  typo fixed in Part B, #1
If you started on section 2.1, save them for the future.
Updated Sunday morning, final form.
Based on the plot below, find all the steady state solutions of the firstorder autonomous ordinary differential equation \(df/dx = H( f )\), and determine the local stability of each. For those steadystates that are stable, determine the set of initial conditions that converge to that steadystate. You may assume $H(f) > 0 for all \(f < 4\) and \(H(f)< 0\) for all \(f > 7\).
Update Monday, Feb 7. Note that we have not coverd Wronskians yet, so don't do the homework questions about them.
Update Monday, Feb 14 to add the two problems from section 3.2.
Our textbook suggests solving 1618 using an algebra program. Sympy is one opensource web program that will do this. Sympy is module for the python programming language, and works best best when you install it on your own computer. But for our purposes, Sympy live is good enough to solve inhomogeneous linear equations by educated guessing with undetermined coefficients. If you know python, you can use the following code example as a guide.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

Formerly due Wednesday, March 2 (updated Monday)
Suppose a mass  spring system has position function \(y(t) = 6e^{−2t} − 3te^{−2t}\) . Compute when the mass passes through the equilibrium position, when it hits its highest point, and then describe how low the mass goes after it hits its highest point.
Suppose a springmass system is undamped, and has a frequency of oscillation equal to \(2\pi\) (in units of Hertz = 1/s). Suppose it begins moving at t = 0 with initial conditions: \(u(0) = −1\) and \(u'(0) = 0\).
Solve the following initialvalue problem using Laplace transforms: \[y'' y'  6y = e^{t}u_4(t), \quad y(0)=0, \quad y'(0)=1.\]
Solve the following initialvalue problem using Laplace transforms: \[y'' + 4 y' + 5y = t u_2(t), \quad y(0)=0, \quad y'(0)=0.\]
For part b, there are many tools. One is to download the java 'pplane' from Alun Lloyd's page Another phaseplane simulator your can run in the browser is at Ariel Barton's, or the version at Geogebra