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Mathematics
Mathematics
Problem
Suppose
∣
f
′
(
x
)
f
(
x
)
f
′
′
(
x
)
f
′
(
x
)
∣
=
0
\begin{vmatrix} f'(x) & f(x) \\ f''(x) & f'(x) \end{vmatrix} = 0
f
′
(
x
)
f
′′
(
x
)
f
(
x
)
f
′
(
x
)
=
0
where
f
(
x
)
f(x)
f
(
x
)
is a continuously differentiable function with
f
′
(
x
)
≠
0
f'(x) \neq 0
f
′
(
x
)
=
0
and satisfies
f
(
0
)
=
1
f(0) = 1
f
(
0
)
=
1
and
f
′
(
0
)
=
2
f'(0) = 2
f
′
(
0
)
=
2
, then
f
(
x
)
=
e
λ
x
+
k
f(x) = e^{\lambda x} + k
f
(
x
)
=
e
λ
x
+
k
, then
λ
+
k
\lambda + k
λ
+
k
is equal to .....
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