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

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Exercise $$\PageIndex{1}$$

What is the order of the following equations

1. $\frac{\partial^3 u}{\partial x^3} + \frac{\partial^2 u}{\partial y^2}=0$
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