Page 59 - Schaum's Outline of Differential Equations

CHAPTER 6

Linear First-Order

Differential Equations

METHOD OF SOLUTION
A first-order linear differential equation has the form (see Chapter .1)

An inlegrating factor for Eq. (6.7) is

which depends onl\ on .v and is independent of v. When both sides of (6.1) are multiplied h\ /(.v), the resulting
equation

is exact. This equation can he solved by ihe method described in Chapter 5. A simpler procedure is to rewrite
(6.3) as

integrate both sides of this last equation \viih respect to.v. and then solve the resulting equation for v.

REDUCTION OF BERNOULLI EQUATIONS

A Bernoulli dilTcrcnlial equation has Ihe form

where n is a real number. The substitution

transforms (6.4) into a linear differential equation in ihe unknown function z(x).

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