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

[itex] x \frac{ \partial u}{ \partial x} + y \frac{ \partial u}{ \partial y}= -x^2u^2[/itex]

2. Relevant equations

3. The attempt at a solution

characteristics are given by

[itex] \frac{ dy}{ dx} = \frac{ y}{ x} [/itex] (a)

and

[itex] \frac{ du}{ dx} = -\frac{x^2u^2 }{ x} [/itex] (b)

So i integrate both equations

but for (a) do i bring the y across which ends up giving ln(y) = ln(x) + k

or leave it where it is and i get y = -yln(x) + k

??

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# Method of characteristics

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