APM346-2021S > Quiz 1

LEC9101 Quiz#1 B Question#2

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Xun Zheng:
Problem 2 (1.5 pt). Find the general solutions to the following equation:
$$u_{xxy}=sin(x)+sin(y)$$


Solution:

Integrating both sides, we get
$$u_{xx}=y sin(x)-cos(y)+f(x)$$
$$u_{x}=-y cos(x)-x cos(y)+F(x)+g(y)$$
$$u(x,y)=-y sin(x)-\frac{x^2}{2}cos(y)+F^{*}(x)+x g(y)+h(y)$$

Victor Ivrii:
not $sin(x)$ but $\sin(x)$ (it is \sin, \cos, \ln, \sum, \int and so on for "math operators")

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