Author Topic: HA2-P4  (Read 597 times)

Victor Ivrii

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Chi Ma

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Re: HA2-P4
« Reply #1 on: September 29, 2015, 01:27:15 AM »
$$u_x+3u_y=xy\\
\frac{dx}{1} = \frac{dy}{3} = \frac{du}{xy}\\
3x-y = C\\
du=xydx=x(3x-C)dx=(3x^2-Cx)dx\\
u = x^3 - \frac{C}{2}x^2 + \phi(3x-y)\\
u = x^3 - \frac{3x-y}{2}x^2 + \phi(3x-y)\\
u|_{x=0}=\phi(-y)=0\\
u = x^3 - \frac{3x-y}{2}x^2=-\frac{1}{2}x^3+\frac{1}{2}x^2y
$$
« Last Edit: October 03, 2015, 05:49:03 AM by Victor Ivrii »

Victor Ivrii

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Re: HA2-P4
« Reply #2 on: October 03, 2015, 05:49:57 AM »
Good. (Sidenote: In LaTeX world double dollars are deprecated)