Page 33 - Schaum's Outline of Differential Equations

16 CLASSIFICATIONS OF FIRST-ORDER DIFFERENTIAL EQUATIONS [CHAR 3

or

2
which is in standard form wi\hf(x, y) = (x + y)/y . There are infinitely many different differential forms associated
with (_/). Four such forms are:
2
(a) Take M(x, y)=x + y, N(x, y) = -y . Then

and (_/) is equivalent to the differential form

(b) TakeMX ;y) = -l, N(x,y) = ——.Then
x + y

and (1) is equivalent to the differential form

(c) Take M(x,y) = , N(x, y Then

and (1) is equivalent to the differential form

(d) Take Then

and (1) is equivalent to the differential form

3.5. Write the differential equation dyldx = ylx in differential form
This equation has infinitely many differential forms. One is

which can be written in form (3.2) as