2.E: Classification of Partial Differential Equations (Exercises)
- Page ID
- 8364
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What is the order of the following equations
- \[\frac{\partial^3 u}{\partial x^3} + \frac{\partial^2 u}{\partial y^2}=0 \nonumber \]
- \[\frac{\partial^2 u}{\partial x^2}-2\frac{\partial^4 u}{\partial x^3 u}+\frac{\partial^2 u}{\partial y^2}=0 \nonumber \]
- Answer
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TBA
Classify the following differential equations (as elliptic, etc.)
- \[\frac{\partial^2 u}{\partial x^2}-2\frac{\partial^2 u}{\partial x \partial y}+\frac{\partial^2 u}{\partial y^2}=0 \nonumber \]
- \[\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2} + \frac{\partial u}{\partial x}=0 \nonumber \]
- \[\frac{\partial^2 u}{\partial x^2}-\frac{\partial^2 u}{\partial y^2} + 2\frac{\partial u}{\partial x}=0 \nonumber \]
- \[\frac{\partial^2 u}{\partial x^2}+ \frac{\partial u}{\partial x}+ 2\frac{\partial u}{\partial y}=0 \nonumber \]
- \[y\frac{\partial^2 u}{\partial x^2}+ x\frac{\partial^2 u}{\partial y^2}=0 \nonumber \]
- Answer
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TBA