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

  • Page ID
    8364
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    Exercise \(\PageIndex{1}\)

    What is the order of the following equations

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

    TBA

    Exercise \(\PageIndex{2}\)

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

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

    TBA


    This page titled 2.E: Classification of Partial Differential Equations (Exercises) is shared under a CC BY-NC-SA 2.0 license and was authored, remixed, and/or curated by Niels Walet via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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