|Class 12 Maths Differential Equations||Homogeneous Function|
A function F(x, y) is said to be homogeneous function of degree n if
F(λx, λy) = λn F(x, y) for any nonzero constant λ.
Eg: F(x, y) = y2 + 2xy
F(λx, λy) = (λy)2 + 2λxλy
F(λx, λy) = λ2 (y2 + 2xy )
Thus, F(x, y) = y2 + 2xy is a homogeneous function.
But, F(x, y) = sin x + cos y is not a homogeneous function since it cannot be expressed as F(λx, λy) = λn F(x, y)