# Toronto Math Forum

## APM346-2022S => APM346--Lectures & Home Assignments => Chapter 1 => Topic started by: asdfghj on January 16, 2022, 07:34:18 PM

Title: chapter 1 Problem 4 (1)
Post by: asdfghj on January 16, 2022, 07:34:18 PM
$uu_{xy}=u_{x}u_{y}$

$(u_{x}u_{y})/uu_{x}=u_{xy}/u_{x}$

divide both side by$uu_{x}$ and get

$u_{y}/u=u_{xy}/u_{x}$

integrate with respect to y

$\ln{u}+f(x)=\ln{u_{x}}+g(x)$ enough to write one function of $x$

let g(x)-f(x)=n(x)

$u=u_{x}\times n(x)$

$u_{x}/u=n(x)$

$\ln{u}=N(x)+m(y)$

$u=N_{1}(x)\times m(y)$ "another $m(x)$"

Title: Re: chapter 1 Problem 4 (1)
Post by: Victor Ivrii on January 17, 2022, 01:29:44 AM
Display formulae are surrounded by double dollars and no empty lines. Multiline formulae use special environments (google LaTeX gather align