2011-49.md

course	course_year	question_number	tags	title	year
Methods	IB	49	IB 2011 Methods	Paper 4, Section I, A	2011

Use the method of characteristics to find a continuous solution $u(x, y)$ of the equation

$$y \frac{\partial u}{\partial x}+x \frac{\partial u}{\partial y}=0$$

subject to the condition $u(0, y)=y^{4}$.

In which region of the plane is the solution uniquely determined?