Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Fall 2016 • Question 9

Question

Math 6410 • ODE Fall 2016 • Question 9

  1. Does a solution of the equation \(u_x+xu_y=u\) with \(u(x,x^2)=x\) exist for \(-\infty <x<\infty \), \(y>0\)? Explain why or why not.
  2. Does a solution of the equation \(xu_x-yu_y=u\) with \(u(x,x^2)=x\) exist for \(-\infty <x<\infty \), \(y>0\)? Explain why or why not.

Raw LaTeX

\begin{enumerate}
\item[(a)] Does a solution of the equation \(u_x+xu_y=u\) with \(u(x,x^2)=x\) exist
for \(-\infty<x<\infty\), \(y>0\)? Explain why or why not.
\item[(b)] Does a solution of the equation \(xu_x-yu_y=u\) with \(u(x,x^2)=x\) exist
for \(-\infty<x<\infty\), \(y>0\)? Explain why or why not.
\end{enumerate}

Topic Tags

Distributions and Weak Solutions Entropy Solutions, Shocks, and Rarefactions Fundamental Solutions Poincare Maps and Periodic Solutions