ABSTRACT
Certain first order differential equations are not of the ‘variable-separable’ type but can be made separable by changing the variable. An equation of the form P
dy dx D Q, where P and Q are functions of both x and
y of the same degree throughout, is said to be homogeneous in y and x. For example, fx, y D x2 C 3xy C y2 is a homogeneous function since each of the three terms are of degree 2. Similarly, fx, y D x 3y
2x C y is homogeneous in x and y since each of the four terms are of degree 1. However, fx, y D x2 y
2x2 C y2 is not homogeneous since the term in y in the numerator is of degree 1 and the other three terms are of degree 2.
