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

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 ×

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

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