Re: F(x,y,y')=0-



ib wrote:

I'm slowly working my way through a high school calculus book. In the chapter on separable differential equations, I have come across the expression F(x,y,y')=0 in the context of, "A separable first-order differential equiation is an equation F(x,y,y')=0 that can be put into the form h(y) dy/dx = g(x)". The expression 'F(x,y,y')=0 ' is new to me and I am asking if someone would kindly provide an explanation of what type of equation this refers to.

thanks,

Ian



F(x,y,y')=0: Commonly known as "Implicit first-order differential equation in the independent variable x and the dependent variable y".

"Implicit" means that all variables and unknowns are =folded into= the LHS, leaving the RHS a constant (by convention zero).
(Implicit: from Latin: implicare = to imply; literally: to fold into)

As pointed out in previous posts, the problem is to find differentiable functions g: x => y=g(x) such that the relation F (x, g(x), dg(x)/dx) = 0 holds.

Johan E. Mebius

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