(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[itex]u\frac{\delta u}{\delta x}[/itex]+[itex]\frac{\delta u}{\delta y}[/itex] =1

[itex]u|_{x=y}=\frac{x}{2}[/itex]

2. Relevant equations

the characteristic equations to solve are:

[itex]\frac{dx}{ds}=u[/itex]

[itex]\frac{dy}{ds}=1[/itex]

[itex]\frac{du}{ds}=1[/itex]

3. The attempt at a solution

I got the following equations from the characteristic equations:

[itex] \frac{dx}{ds}=u[/itex] means [itex]\frac{d^2x}{ds^2}=\frac{du}{ds}=1[/itex]

after integrating twice i get [itex]x=\frac{1}{2}s^2+ks+x_0[/itex]

[itex] y = s +y_{0} [/itex]

[itex] u = s +u_{0} [/itex]

and here is where I am now stuck.

I also dont know how to apply the condition given : [itex]u|_{x=y}=\frac{x}{2}[/itex]

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# Homework Help: Solve by Method of Characteristics

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