Order of a differential equation refers to highest derivative, not function degree

[tandoorichicken]

Okay! Just making sure I have the concept of orders in differential equations right. So the order refers to the highest order of the derivatives, not the actual functions right?

So a function like y + yy' = ? would be first order, y + y'' would be second order, but something like y^4 +3yy' would still be first order right?

 

[jamesrc]

Yep, you've got it.

 

[dextercioby]

The "order of the functions" (the power that "y" or its derivatives have in the ODE) gives the nonlinear character...

Daniel.

 

[quasar987]

I guess it's preferable to talk about the "degree of the ODE" instead of the "order of the function or its derivative". If degree > 1, the ODE is nonlinear.

 

[HallsofIvy]

The "order of the functions" (the power that "y" or its derivatives have in the ODE) gives the nonlinear character...

That's "degree". Though the original post should have referred to "order of the diffential equation", not "order of the function".