Example 26 Find the particular solution of the differential equation log
3
4
dy
x
y
⎛dx
⎞ =
+
⎜
⎟
⎝
⎠
given that y = 0 when x = 0 Solution The given differential equation can be written as
dy
dx  = e(3x + 4y)
or
dy
dx  = e3x e4y (1)
Separating the variables, we get
edy4 y
= e3x dx
Therefore
e4 y
dy
∫−
=
3x
e dx
∫
Fig 9