A First Course in Differential Equations

(a) Use the Laplace transform and the information given in Example 3 to obtain the solution (8) of the system […]

(a) Now suppose that air resistance is a retarding force tangent to the path but acts opposite to the motion. If

(a) A projectile, such as the canon ball shown in Figure 7.R.13, has weight w = mg and initial velocity

In Problem 27 in Chapter 5 in Review we examined a spring/mass system in which a mass m slides over

(a) Suppose two identical pendulums are coupled by means of a spring with constant k. See Figure 7.R.12. Under the

When a uniform beam is supported by an elastic foundation, the differential equation for its deflection y(x) is where k

(a) Laguerre’s differential equation ty” + (1 – t)y’ + ny = 0 is known to possess polynomial solutions when

In Section 6.4 we saw that ty” + y’ + ty = 0 is Bessel’s equation of order n =

Reread Example 4 in Section 3.1 on the cooling of a cake that is taken out of an oven. (a)

Appropriately modify the procedure of Problem 68 to find a solution of y” + 3y’ –  4y = 0, y(0)