Setting up and integrating Problem set B Answers

1. (a) \(\dfrac{dC}{dt}=kC\)
2. (b) \(\dfrac{dA}{dt}=kA^{1/4}\)

1. (a) \(\dfrac{dd}{dt}=\dfrac{k}{d}\)
2. (b) \(\dfrac{dl}{dt}=\dfrac{k}{l^2}\)

1. (a) \(\dfrac{dV}{dt}=-kV^{1/3}\)
2. (b) \(\dfrac{dI}{dt}=-\dfrac{k}{I}\)

1. (a) \(y=-20 \sqrt{x} + x^{4}+c\)
2. (b) \(y=-18e^{-\frac{t}{3}}+c\)
3. (c) \(y=-3t + 12 \ln|t|+c\)
4. (d) \(s=-\frac{3 \cos(4t)}{4}+c\)

\(\dfrac{dJ}{dt}=kJ(800-J)\)

\(\dfrac{dJ}{dt}=\dfrac{kJ(900-J)}{t}\)

1. (a) \(h=-20e^{-\frac{t}{4}}+c\)
2. (b) 17.3 m

1. (a) \(F=4m + \frac{3}{m}+c\)
2. (b) \(G=2t + 2e^{-3t}+c\)