Notation Q: What Does F(y/x) Mean?

[theperthvan]

Hi, Just a question on notation. What does $$F(\frac{y}{x})$$ mean?

It is in the context of..."the differential equation $$y' = F(\frac{y}{x})$$ can be solved dadadadada..."

Cheers,

 

[slider142]

It just means the right-hand side is a function of y/x. This could be a constant function, like F(y/x)=0, which would be trivial and silly, or something like F(y/x) = (y/x)^2 + (1/2)(y/x). Basically, if you can rearrange the right-hand side of the equation to explicitly be a function of y/x, whatever follows in your text will hold.
For example, if you have the equation y' = x + 2, there is no way to write the right-hand side as a function of y/x. Writing it as y' = x*(y/x)*(y/x)^(-1) + 2 still includes x independently, so whatever follows that sentence in your book will not work for this type of equation.