APM346-2022S > Chapter 1

home assignment1 Q3(1),(2),(3)&(4)


$u_{xy}=0,denote: v=u_{x}$
$u=F(x)+g(y), (let F'(x)=f(x))$

let$ u_{x} = v$, so
$ u_{xy}=v_{y}$
$therefore: v_{y}=v$ integrate on both sides
$v=u_{x}=e^{2y}\times f_2(x)$
let $f_{2}(x)=e^{f_{1}(x)}$
$u=f_{3}(x)\times e^{2y}+g(y)$
where $f'_{3}(x)=f_{2}(x)$


 integrate on both sides
the general solution is :
$u=u^2+x\times e^{xy}+F(y)+g(x)$

Victor Ivrii:
OK. Remarks:

1. Do not use $*$ as a multiplication sign!
2. Do not use LaTeX for italic text (use markdown of the forum--button I)
3. Escape ln, cos, .... : \ln (x) to produce $\ln (x)$ and so on


[0] Message Index

Go to full version