# Is this a differential equation?

My textbook says that:

"A differential equation contains both the function and the derivative of the function"

and at the same time claims that y'=3x2 is a differential equation.

How can this be? The original function isnt part of the equation in this case?

Simon Bridge
Homework Helper
Yes it is. y'=3x2 is the same as y'+0y=3x2 (the coefficient of y is zero) and also the same as:
xy'=3y

But I think you need to take the text book a little less seriously.
What they mean is that if g(x)=f(x,y,y',y''...) then g is a DE.
As you learn more the definition will get expanded to include more cases.

1 person
HallsofIvy
It is a particularly easy differential equation- y is simply the anti-derivative of $$3x^2$$. I would say the statement "A differential equation contains both the function and the derivative of the function" is at best misleading. The derivative of the function must appear explicitly in the equation. The function itself does not have to be explicitly in the equation.