Discussion
The partial differential equation
\(u_{t} + u_{x} = u^{2}\)
can be classified as :
Answer: C
The equation is semilinear.
A first-order PDE is semilinear when the derivatives appear linearly with coefficients depending only on the independent variables, while the remaining term may depend non-linearly on \(u\). In \(u_{t} + u_{x} = u^{2}\) the derivative part \(u_{t} + u_{x}\) is linear with constant coefficients, and the non-linearity is only in \(u^{2}\).
It is not linear, because of \(u^{2}\). It is non-linear in the broad sense, but the standard classification (linear, semilinear, quasilinear, fully non-linear) places it in the more specific class of semilinear equations.
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