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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.