(A) (4x + 6y + 5) dy – (3y + 2x + 4) dx = 0
(B) (xy) dx – (x3 + y3) dy = 0
(C) (x3 + 2y2) dx + 2xy dy = 0
(D) y2 dx + (x2 – xy – y2) dy = 0
9 5 3  Linear differential equations
A differential equation of the from
P
dy
dx +y
 = Q
where, P and Q are constants or functions of x only, is known as a first order linear
differential equation 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