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Initial Value Problem and Method of Characteristics

Solve the following initial data problem:

u_x + u_y = u^2
u(x,0) = h(x)

I have that x_t = 1, y_t = 1 and z_t = z^2
also, x(0) = s, y(0) = 0 and z(0)=h(s)

from this I have x=s + t and y=t

Please provide a detailed solution of how to find z.

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