Equations Composed of Homogeneous Functions

A function f(x,y) is said to be homogeneous of degree n if there exists a constant n such that for every parameter A 

the functions x + xy and tan ix/y) are both homogeneous, the first of degree 2 and the second of degree 0. However, the function iy + x) is not homogeneous. 

This implies that first order equations composed of homogeneous functions can always be arranged in the form 

This form is easy to remember, since the dimensional ratio y/x appears throughout. The occurrence of this ratio suggests the substitution y/x = vix). 

This is an implicit relation between y and x, which is typical of nonlinear solutions. 

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