Toronto Math Forum
APM3462021S => APM346Tests & Quizzes => Quiz 1 => Topic started by: Xun Zheng on January 28, 2021, 03:35:12 PM

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

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