Skip to main content
\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)
Mathematics LibreTexts

2.E: Classification of Partial Differential Equations (Exercises)

  • Page ID
    8364
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    Exercise \(\PageIndex{1}\)

    What is the order of the following equations

    1. \[\frac{\partial^3 u}{\partial x^3} + \frac{\partial^2 u}{\partial y^2}=0\]
    2. \[\frac{\partial^2 u}{\partial x^2}-2\frac{\partial^4 u}{\partial x^3 u}+\frac{\partial^2 u}{\partial y^2}=0\]
    Answer

    TBA

    Exercise \(\PageIndex{2}\)

    Classify the following differential equations (as elliptic, etc.)

    1. \[\frac{\partial^2 u}{\partial x^2}-2\frac{\partial^2 u}{\partial x \partial y}+\frac{\partial^2 u}{\partial y^2}=0\]
    2. \[\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2} + \frac{\partial u}{\partial x}=0\]
    3. \[\frac{\partial^2 u}{\partial x^2}-\frac{\partial^2 u}{\partial y^2} + 2\frac{\partial u}{\partial x}=0\]
    4. \[\frac{\partial^2 u}{\partial x^2}+ \frac{\partial u}{\partial x}+ 2\frac{\partial u}{\partial y}=0\]
    5. \[y\frac{\partial^2 u}{\partial x^2}+ x\frac{\partial^2 u}{\partial y^2}=0\]
    Answer

    TBA