12.2 可分离变量的微分方程与一阶线性微分方程

.
,
)
(
3
)
(
)
(
2
2
2
2
3
2
2
2
∫∫∫
≤
+
+
+
+
+
=
t
z
y
x
t
dV
z
y
x
f
t
f
t
f
).
(
,
0 t
t f
≥
3
2
0
0
2
0
sin
)
(
3
)
( t
dr
r
r
f
d
d
t
f
t
+
⋅
= ∫
∫
∫
ϕ
ϕ
θ π
π
3
0
2
0
)
(
)
cos
(
6 t
dr
r
f
r
t
+
⋅
−
= ∫
π
ϕ
π
3
0
2
)
(
12 t
dr
r
f
r
t
+
= ∫
π
?
)
( =
t
f
0.
(0)
,
3
)
(
12
)
(
2
2
=
+
=
′ f
t
t
f
t
t
f
π