Differential Equations         Study Guide for Hour Quiz #3        C.S.Davis

You are responsible for the subject matter from Zill and Cullen (sixth edition)  in sections 4.7, 4.8, 5.1, 6.1, and 6.3. The following topics are notable in their importance.

4.7  1. Solve the Cauchy Euler differential equation.   P178#1-7 odd

4.8  1. Solve systems of linear DE=s and IVP=s (Differential Operator Method)  (This method involves converting from a system of first order IVP's to a higher order IVP) P182#1-9 odd 
       2. Convert from a higher order IVP  to a system of first order IVP's in normal form.   (class notes)

5.1  1. Solve spring problems
             a. Free undamped spring motion - (harmonic motion)   P207#3,9,11
             b. Free damped spring motion.   P208#21,23,25,27
             c. Driven spring motion (undamped and damped) , resonance.   P209#29,31
       2. Solve electric circuits problems: LRC series circuits.   P211#45,47,49

6.1,6.3 
       1. For a LHContC, be able to find using the power series method to find
             a. The power series general solution to a given DE.   P248#19,21,29
             b. The power series solution to an IVP.   (No assignment from text.  Solve the three IVP's below.)

Supplementary problems not in Zill: Solve these IVP=s by power series.

Hermite's Equation:        y'' - 2(x - 1)y' + 2y = 0, y(1) = 0, y'(1) = 1.

Chebyshev's Equation:        (1 - x²)y'' - xy' + y = 0, y(0) = 0, y'(0) = 1.

Legendre's Equation:        (1 - x²)y'' - 2xy' + 6y = 0, y(0) = 1, y'(0) = 0.