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**PDE--initial condition**

## Homework Statement

Solve the equation [tex]u_x+2xy^2u_y=0[/tex] with [tex]u(x,0)=\phi (x)[/tex]. Strauss PDE 2nd ed., chapter 1.5, exercise 6.

## Homework Equations

The question is under "Well-Posed Problems" section, so this might be about existence, uniqueness, or stability.

## The Attempt at a Solution

I can easily solve the first order PDE without the constaint, and get the solution as [tex]u(x,y)=f(x^2+\frac{1}{y})[/tex]. However, when I try to apply the initial condition, since y=0 there, I got stuck. I cannot really interpret this situation, so I need your help.