Consider the initial value problem $\frac{dy}{dx} = -3y$ with $y(0) = 4$. What is the value of $y$ at $x = \frac{\ln 2}{3}$?

Answer Key:

2

### Solution: Solution is $y(x) = y(0)e^{-3x} = 4e^{-3x}$. At $x = \frac{\ln 2}{3}$, $y = 4e^{-\ln 2} = 4 \times \frac{1}{2} = 2$. Correct: 2.

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