Page 62 - Schaum's Outline of Differential Equations

CHAP. 6] LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS 45

Multiplying the differential equation by I(x), we obtain

or

Upon integrating both sides of this last equation, we have

whereupon

6.1 Solve the initial-value problem1.
The solution to this differential equation is given in Problem 6.10 as

Applying the initial condition directly, we have

6.12. Solve

This is a linear differential equation for the unknown function i(x). It has the form of Eq. (6.1) with y replaced
by z. The integrating factor is

Multiplying the differential equation by I(x), we obtain

or

Upon integrating both sides of this last equation, we have

whereupon

6.13. Solve

This is a linear differential equation for the unknown function Q(t). It has the form of Eq. (6.1) with y replaced
by Q, x replaced by t, p(t) = 21(10 + 2t), and q(t) = 4. The integrating factor is