- #1
WannaBe22
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Homework Statement
Let [tex] f(x,y) [/tex] be the soloution of [tex]xu_x +yu_y = u^4 [/tex] that is defined in the whole plane. Prove that [tex] f = 0 [/tex] .
Hint: Think of the characteristic curves of this PDE.
HOPE You'll be able to help me
Thanks in advance!
Homework Equations
The Attempt at a Solution
By trying to solve this problem, I've got this subidinary equations:
[tex] \frac{dx}{x} = \frac{dy}{y} = \frac{du}{u^4} [/tex] . From these equations we will receive: [tex] y=c_1 \cdot x [/tex] and [tex] u^3 = \frac{1}{-3ln(x)-3c_s} [/tex] ... But can it help us? I think we are missing this way a few other soloutions...
Help is needed!
Thanks !