Page 3 - CH 9 Differential Equation Lession Notes

Integrating both sides, we get,

which is the required solution of (i).
9.5.2 Homogeneous differential equations

A function F(x, y) is said to be homogeneous function of degree n if ( ) ( )
for any nonzero constant .

Note: A differential equation of the form ( ) is said to be homogenous if

F(x, y) is a homogenous function of degree zero.
We make the substitution y = v.x

A differential equation of the form ( ) is said to be homogenous if

F(x, y) is a homogenous function of degree zero.
We make the substitution x = v.y

Example: Solve the equation:

Sol :

We have,

(i)
Put y = vx

Then,
From (i), we get