Toronto Math Forum

APM346-2015F => APM346--Home Assignments => HA2 => Topic started by: Victor Ivrii on September 28, 2015, 01:02:27 PM

Title: HA2-P4
Post by: Victor Ivrii on September 28, 2015, 01:02:27 PM

http://www.math.toronto.edu/courses/apm346h1/20159/PDE-textbook/Chapter2/S2.1.P.html#problem-2.1.P.4 (http://www.math.toronto.edu/courses/apm346h1/20159/PDE-textbook/Chapter2/S2.1.P.html#problem-2.1.P.4)

Title: Re: HA2-P4
Post by: Chi Ma on September 29, 2015, 01:27:15 AM

$$u_x+3u_y=xy\\
\frac{dx}{1} = \frac{dy}{3} = \frac{du}{xy}\\
3x-y = C\\
du=xydx=x(3x-C)dx=(3x^2-Cx)dx\\
u = x^3 - \frac{C}{2}x^2 + \phi(3x-y)\\
u = x^3 - \frac{3x-y}{2}x^2 + \phi(3x-y)\\
u|_{x=0}=\phi(-y)=0\\
u = x^3 - \frac{3x-y}{2}x^2=-\frac{1}{2}x^3+\frac{1}{2}x^2y
$$

Title: Re: HA2-P4
Post by: Victor Ivrii on October 03, 2015, 05:49:57 AM

Good. (Sidenote: In LaTeX world double dollars are deprecated)