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 6
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DIFFERENTIAL EQUATIONS
417
or
4
4
y
e−
−
 =
3
C
3
ex
+
or
4 e3x + 3 e– 4y + 12 C = 0