Toronto Math Forum

APM346-2021S => APM346--Tests & Quizzes => Quiz 1 => Topic started by: Xun Zheng on January 28, 2021, 03:35:12 PM

Title: LEC9101 Quiz#1 B Question#2
Post 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
$$u_{xx}=y sin(x)-cos(y)+f(x)$$
$$u_{x}=-y cos(x)-x cos(y)+F(x)+g(y)$$
$$u(x,y)=-y sin(x)-\frac{x^2}{2}cos(y)+F^{*}(x)+x g(y)+h(y)$$

Title: Re: LEC9101 Quiz#1 B Question#2
Post by: Victor Ivrii on January 28, 2021, 08:01:17 PM
not $sin(x)$ but $\sin(x)$ (it is \sin, \cos, \ln, \sum, \int and so on for "math operators")