Differential Equations: Orders Explained

AI Thread Summary
The order of a differential equation is determined by the highest derivative present, not the functions themselves. For example, y + yy' is first order, y + y'' is second order, and y^4 + 3yy' remains first order. The term "degree" is preferred to describe the power of the functions or derivatives, indicating nonlinearity when degree is greater than one. It's important to clarify that the discussion should focus on the "order of the differential equation" rather than the "order of the function." Understanding these distinctions is crucial for analyzing differential equations accurately.
tandoorichicken
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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?
 
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Yep, you've got it.
 
The "order of the functions" (the power that "y" or its derivatives have in the ODE) gives the nonlinear character...

Daniel.
 
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.
 
dextercioby said:
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".
 

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