Suppose where is a continuously differentiable function with and satisfies and

MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations

Problem

Suppose

\begin{vmatrix} f'(x) & f(x) \\ f''(x) & f'(x) \end{vmatrix} = 0

where

f(x)

is a continuously differentiable function with

f'(x) \neq 0

and satisfies

f(0) = 1

and

f'(0) = 2

, then

f(x) = e^{\lambda x} + k

, then

\lambda + k

is equal to .....