APM346--2020S > Quiz 1

Quiz1 TUT5101

(1/1)

Jingjing Cui:
Question 1: $u_{xx}+u_{xxyy}+u=0$

This is a 4th order linear homogeneous equation since all the terms in the equation are related to u and the operator of the equation $\frac{d^2u}{dx^2}+\frac{d^2u}{dx^2}\frac{d^2u}{dy^2}+1$ is linear.

Question 2: Find the general solution for $u_{xyz}=xy\\ u_{xy}=xyz+f(x,y)\\ u_{x}=\frac{1}{2}xy^2z+F(x,y)+g(x,z)\\ u=\frac{1}{4}x^2y^2z+\hat{F}(x,y)+G(x,z)+h(y,z)$

Victor Ivrii:
Correct. Please write partial derivatives as $\frac{\partial u}{\partial x}$ etc