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˙x = e t−x /x x(α) = 1 α ∈ R
α < 0 g g
xα g(xα) = 0 (xα−1)e xα =
−e α 0 < xα < 1 e α > 0 g(x) > 0 x > xα
tα = lim log g(x) = −∞
x→(xα) +
t → −∞ xα
t ≥ α t → +∞ +∞ x = x(t)
t → +∞ e t = (x − 1)e x α > 0 ] log(e α − 1), +∞[
t → t + α = log(e α − 1) + 0 tα < α α = 0
R t → −∞ 0 α < 0 R t → −∞
0 < xα < 1 xα (xα − 1)e xα = −e α
˙x = x 2 /(1 − tx) x(0) = α α ∈ R
ω(t, x) = p(t, x) dx + q(t, x) dt = (1 − tx) dx − x 2 dt = 0.
∂tp(t, x) − ∂xq(t, x) = −x + 2x = x = 0 ω
∂tp(t, x) − ∂xq(t, x) = x = f(x)q(t, y) − g(t)p(t, y)