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Actually it's confusing me, somewhere it is written non-homogeneous and somewhere inhomogeneous.

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1 Answer

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First let me say that “in homogeneous” and “non homogeneous” means the same thing. But I suspect you already know this.

A homogeneous differential equation is one where every term involves derivatives of the dependent variable and (though not necessary) terms containing the dependent variable itself. For example

$$\frac{d^2 f}{dx^2} + \frac{d^2 f}{dy^2} + 7f =0$$

is called homogeneous.

A non homogeneous differential equation involves derivatives of the dependent variable with terms containing the independent variable(s). For example

$$\frac{d^2 f}{dx^2} + \frac{d^2 f}{dy^2} + f = x^2 + xy$$

is a non homogeneous differential equation.

So if you hear your teacher/lecturer say “in homogeneous” and “homogeneous” or even “non homogeneous” do not be confused since he/she means the distinction between “homogeneous” and “non homogeneous”.

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