Page 60 - Schaum's Outline of Differential Equations

CHAP. 6] LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS 43

Solved Problems

6.1. Find an integrating factor for y' — 3y = 6.
The differential equation has the form of Eq. (6.1), withp(x) = -3 and q(x) = 6, and is linear. Here

so (6.2) becomes

6.2. Solve the differential equation in the previous problem.
Multiplying the differential equation by the integrating factor defined by (1) of Problem 6.1, we obtain

Integrating both sides of this last equation with respect to x, we have

6.3. Find an integrating factor for y' - 2xy = x.
The differential equation has the form of Eq. (6.1), with p(x) = -2x and q(x) = x, and is linear. Here

so (6.2) becomes

6.4. Solve the differential equation in the previous problem.
Multiplying the differential equation by the integrating factor defined by (1) of Problem 6.3, we obtain

Integrating both sides of this last equation with respect to x, we find that

4
6.5. Find an integrating factor for y' + (4lx)y = x .
4
The differential equation has the form of Eq. (6.1), with p(x) = 4/x and q(x) = x , and is linear. Here