homogeneous first-order differential equation

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A first-order differential equation dy/dx=f(x, y) in which the function f, of two variables, has the property that f(kx, ky)=f(x, y) for all k. Examples of such functions areAny such function f can be written as a function of one variable v, where v=y/x. The method of solving homogeneous first-order differential equations is therefore to let y=vx so that dy/dx=xdv/dx+v. The differential equation for v as a function of x that is obtained is always separable.

Subjects: Mathematics.

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