Further,  the equation must be free from m and c because m and
Fig 9 1
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DIFFERENTIAL EQUATIONS
387
X
X’
Y
Y’
y = x+1
y = x
y = –x
y = –x–1
y =
x
3
O
c are different for different members of the family This is obtained by differentiating equation (5) with
respect to x, successively we get
dy
dx =m
, and 
2
2
0
d y
dx
= (6)
The equation (6) represents the family of straight
lines given by equation (5)