- #1
gtfitzpatrick
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Homework Statement
x([itex]\partial u / \partial x [/itex]) + y([itex]\partial u / \partial y [/itex]) = -[itex]x^2u^3[/itex]where u(x,1) = x for -[itex]\infty[/itex] < x < [itex]\infty[/itex]
Homework Equations
The Attempt at a Solution
dy/dx = y/x
= ln(y)=ln(x)+k k=constant of integration
=[tex] y = x + e^K[/tex]
=y=x+k
along this characteristic
[tex]du/dx = -(x^2u^3)/x[/tex]
= [tex]-xu^3[/tex]
= [tex]1/(2u^2) = ln(x) + F(K) [/tex]
not sure where to go from here...
should i simplify more for u and swap in k=y-x then use the conditions?