Which of the following is a homogeneous differential equation?

A.

B.

C.

D. $y^{2} d x + (x^{2} - x y - y^{2}) d y = 0$

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Solution

Function F(x, y) is said to be the homogenous function of degree n, if

F(λx, λy) = λⁿ F(x, y) for any non-zero constant (λ).

Consider the equation given in alternativeD:

Hence, the differential equation given in alternative D is a homogenous equation.

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