MHB Meaning of Symbols in Differential Equation

[paulmdrdo]

just want to know what these symbols mean

$\displaystyle M(x,y)\,dx+N(x,y)\,dy=0$

$\displaystyle \frac{dy}{dx}=f(x,y)$

$\displaystyle F(x,y,y'...y^n)=0$

what's M and N and the ordered pair (x,y) mean here.

I don't understand my book. please explain.

 

[Sudharaka]

Re: meaning

just want to know what these symbols mean

$\displaystyle M(x,y)\,dx+N(x,y)\,dy=0$

$\displaystyle \frac{dy}{dx}=f(x,y)$

$\displaystyle F(x,y,y'...y^n)=0$

what's M and N and the ordered pair (x,y) mean here.

I don't understand my book. please explain.

Hi LATEBLOOMER, :)

It means that $M$ and $N$ are functions which depend on $x$ and $y$. For example, $M(x,\,y)=4xy+x^2 \mbox{ and }N(x,\,y)=3xy-y^2$.

 

[HallsofIvy]

Re: meaning

just want to know what these symbols mean

$\displaystyle M(x,y)\,dx+N(x,y)\,dy=0$

$\displaystyle \frac{dy}{dx}=f(x,y)$

$\displaystyle F(x,y,y'...y^n)=0$

what's M and N and the ordered pair (x,y) mean here.

I don't understand my book. please explain.

There is NO "ordered pair (x, y)". That simply indicates that M, N and f are functions of the two variables x and y.