A First Course in Differential Equations

In this problem you are led through the commands in Mathematica that enable you to obtain the symbolic Laplace transform […]

Because f(t) = ln t has an infinite discontinuity at t = 0 it might be assumed that ℒ{ln t} does not

(a) Use (1) to find the general solution of Use a CAS to find eAt. Then use the computer to

Assume w2 = 3/4 that in (4). Use the resulting secondorder Runge-Kutta method to approximate y(0.5), where y(x) is the

Use the RK4 method with h = 0.1 to approximate y(0.5), where y(x) is the solution of the initial-value problem

(a) Solve (2) of Section 7.6 using the first method outlined in the Remarks (page 345)—that is, express (2) of

Solving a nonhomogeneous linear system X’ = AX + F(t) by variation of parameters when A is a 3 ×

Repeat Problem 19 using the improved Euler’s method, which has global truncation error O(h2). See Problem 5. You might need

Repeat Problem 17 for the initial-value problem y’ = e-y, y(0) = 0. The analytic solution is y(x) = ln(x

Repeat Problem 17 using the improved Euler’s method, which has a global truncation error O(h2). See Problem 1. You might