Mathematics
OpenStudy (anonymous):

What does it mean for a differential equation to be homogenous? I don't quite understand the notation in the definition.

I believe it basically means that if you add together a set of solutions, you still get a solution, and multiples of solutions are likewise solutions to the differential equation. Hope someone else can expand further :)

OpenStudy (anonymous):

So how can I recognize a homogenous equation?

OpenStudy (anonymous):

If a differential equation is in terms of y (i.e. y'' + y' + y, etc.), it is said to be homogeneous as long as there is no term without a y. So for example $$\frac{dy}{dx} + y = 0$$ is homogeneous, but $$\frac{dy}{dx} + y = 13$$ is not, because the 13 is not in terms of the y.