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Q0 Q2 Q1
Q1 Q1
−(1, ˙x)
ˆn1 · (−1, − ˙x) t=1/(2x)+x2 = 1
> 0,
2x2 Q1 t < 0
y(t) = x(−t) x(t)
y(t) ˙y = − ˙x(−t) = −(−t − y 2 (t)) = t + y 2 (t)
¯ε = ¯ε(a) 0 < ε < ¯ε(a) y(t) |t| < ε 2
t > ε 2
˙y > ε 2 + y 2 ˙z = z 2 + ε 2 z(0) = a
1 z
1
arctan = t + C, C =
ε ε ε
z(t)
t ∗ =
π/2 − arctan a
ε
ε
a
arctan , z(t) = ε tan
ε
> 0, lim z(t) = +∞,
t→t∗−
εt + arctan a
.
ε
y(t) 0 < t1 < t ∗ x(t)
t = −t1 < 0
x(t) {(t, x) : t < 0}
+∞ −∞
t ≥ 0 a ≥ 0
t > 0 t = x 2 R
γ R +∞ Q0
R
t > 0 √ t
˙x
t
= 1 − x2
t .
t ˙x(t) x(t)
Q0 x 2 (t)/t 1 x(t)
√ t
Q2 a < − 3 1/2 t > 0
R −∞
Q2 −∞
Q2 t > 0
0 < t < 1 ˙x < 1 − x 2 ˙z = 1 − z 2 z(0) = a
t = t∗ < 1
1 1 1 1 1 1
= dz + dz =
1 − z2 2 1 − z 2 1 + z 2 log
1 − z
1
+ z
1
2 log
1 + z
1
− z = t + C.
z → ±∞ t + C → 0 t∗ = −C
C = 1
2 log
1 + a
1
− a
.
0 < − 1
2 log
1 + a
1
− a
< 1