Mathematics 376: Ordinary Differential Equations
Assignment 2
Note: This assignment consists of 5 problems of equal weight.
Due: After Unit 9
1. Given an interval x > 0 and the function set
S = {ln(x5), ln 5, 4 ln(x), ln(5x)},
construct a linear ODE of lowest order such that each function in S is one of the set’s solutions on the interval.
2. Reduce the system of first-order equations given below to a single equation of higher order and solve that equation. Use the method of undetermined coefficients.
3. Given the equation
in standard form. (see p. 319 of the textbook), where L is a linear operator of the second order with fundamental solution set {x, x2}, find the general solution.
4. Use the method of variation of parameters to solve
5. (Transient Current)
An RLC series circuit has a voltage source given by E(t) = 20 sin(t) V, an inductor of 3 H, a resistor
6 Ω, and a capacitor of 3/1F. Find the current I(t) in this circuit fort > 0 if
I(0) = 2, I' (0) = 0.
Find the moment of time when the transient current is equal to zero.