We will now discuss the solutions of differential equations which are
of the fi rst order but are of degree higher than one. Such differential
equations will contain only the fi rst order differential coeffi cient
dy
dx
but
will occur in a degree higher than one. It is usual to denote
dy
dx
by p. The
general form of such a differential equation is then
p
n
+A
1
p
n−1
+A
2
p
n−2
+ … +A
n−1
p +A
n
= 0
where A
1
, A
2
… A
n
are some functions of x and y.
Now we will consider various methods of solving the differential
equations of the above type.
4.1 EQUATIONS SOLVABLE FOR p
Suppose the dif ...
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