What is the minimum value of the solution to the differential equation $\frac { d y } { d x } = y \cos x$ with $y ( 0 ) = 6$ ?
A)6
B)0
C) $6$ /e
D) $6$ e

Question

Quizplus · Accepted Answer

The differential equation $\frac { d y } { d x } = y \cos x$ is a first-order linear ordinary differential equation. Its solution, given the initial condition $y(0) = 6$, can be found using the method of integrating factors. The solution to this differential equation is $y = 6e^{\sin x}$. The minimum value of $e^{\sin x}$ occurs when $\sin x = -1$, which gives $e^{-1} = \frac{1}{e}$. Therefore, the minimum value of the solution is $6 \cdot \frac{1}{e} = \frac{6}{e}$.

What Is the Minimum Value of the Solution to the Differential