Consider the initial value problem $\frac{dy}{dx} + 3y = 0$ with $y(0) = 4$. What is the value of $y(\ln 2)$? (Round off to two decimal places).

Answer Key:

0.50

### Solution: General solution is $y(x) = C e^{-3x}$. With $y(0) = 4$, $y(x) = 4 e^{-3x}$. For $x = \ln 2$, $y = 4 e^{-3 \ln 2} = 4 e^{\ln(2^{-3})} = 4 \times \frac{1}{8} = 0.5$. Correct: 0.50 (range 0.49 to 0.51).

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