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FirstOrder Partial Differential Equations >
Quasilinear Partial Differential Equations
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2. FirstOrder Quasilinear Partial Differential Equations
2.1. Equations of the Form f(x, y)w_{x} + g(x, y)w_{y} = h(x, y, w)

w_{x} + aw_{y} = f(x)w + g(x)w^{k}.

w_{x} + aw_{y} = f(x) + g(x)e^{λw}.

aw_{x} + bw_{y} = f(w).

aw_{x} + bw_{y} = f(x)g(w).

w_{x} + aw_{y} = f(x)g(y)h(w).

axw_{x} + byw_{y} = f(w).

ayw_{x} + bxw_{y} = f(w).

ax^{n}w_{x} + by^{k}w_{y} = f(w).

ay^{n}w_{x} + bx^{k}w_{y} = f(w).

ae^{λx}w_{x} + be^{βy}w_{y} = f(w).

ae^{λy}w_{x} + be^{βx}w_{y} = f(w).

f(x)w_{x} + g(y)w_{y} = h(w).

f(y)w_{x} + g(x)w_{y} = h(w).
2.2. Equations of the Form w_{x} +
f(x, y, w)w_{y} = 0

w_{x} + [aw + yf(x)]w_{y} = 0.

w_{x} + [aw + f(y)]w_{y} = 0.

w_{x} + f(w)w_{y} = 0.

w_{x} + [f(w) + ax]w_{y} = 0.

w_{x} + [f(w) + ay]w_{y} = 0.

w_{x} + [f(w) + g(x)]w_{y} = 0.

w_{x} + [f(w) + g(y)]w_{y} = 0.

w_{x} + [yf(w) + g(x)]w_{y} = 0.

w_{x} + [xf(w) + yg(w) + h(w)]w_{y} = 0.

w_{x} + f(x)g(y)h(w)w_{y} = 0.
2.3. Equations of the Form w_{x} +
f(x, y, w)w_{y} = g(x, y, w)

w_{x} + aww_{y} = f(x).

w_{x} + aww_{y} = f(y).

w_{x} + [aw + f(x)]w_{y} = g(x).

w_{x} + f(w)w_{y} = g(x).

w_{x} + f(w)w_{y} = g(y).

w_{x} + f(w)w_{y} = g(w).

w_{x} + [f(w) + g(x)]w_{y} = h(x).

w_{x} + [f(w) + g(x)]w_{y} = h(w).

w_{x} + [f(w) + yg(x)]w_{y} = h(x).

w_{x} + f(x, w)w_{y} = g(x).

w_{x} + f(x, w)w_{y} = g(w).
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