Solve $u_x + 2u_y = u^2$, $u(x, 0) = h(x)$.
Added by Edward J.
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This is a standard second-order linear homogeneous differential equation with constant coefficients. The characteristic equation is rĀ² + 2 = 0, which has roots r = Ā±ā2i. The general solution to the homogeneous equation is u(x) = cācos(ā2x) + cāsin(ā2x), where cā Show moreā¦
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