Some examples of the first order linear differential equation are
dy
dx +y
 = sin x
1
dy
y
dx
⎛x
⎞
+ ⎜
⎟
⎝
⎠
 = ex
log
dy
y
dx
x
x
⎛
⎞
+ ⎜
⎟
⎝
⎠
 = 1
x
Another form of first order linear differential equation is
1P
dx
x
dy +
 = Q1
where, P1 and Q1 are constants or functions of y only Some examples of this type of
differential equation are
dx
dy +x
= cos y
2
dx
x
dy
+−y
 = y2e – y
To solve the first order linear differential equation of the type
P
dy
y
dx  
 = Q (1)
Multiply both sides of the equation by a function of x say g (x) to get
g(x) dy
dx  + P (g(x)) y = Q