Setting up and integrating Problem set A Answers

1. (a) \(\dfrac{dM}{dt}=kM\)
2. (b) \(\dfrac{dh}{dt}=kh^{1/3}\)

1. (a) \(\dfrac{dx}{dt}=\dfrac{k}{x}\)
2. (b) \(\dfrac{dr}{dt}=\dfrac{k}{r^3}\)

1. (a) \(\dfrac{dN}{dt}=-k\sqrt N\)
2. (b) \(\dfrac{dv}{dt}=-\dfrac{k}{v^2}\)

1. (a) \(y=12 \sqrt{x} + \frac{x^{4}}{2}+c\)
2. (b) \(y=-10e^{-\frac{t}{2}}+c\)
3. (c) \(y=2t + 8 \ln|t|+c\)
4. (d) \(s=2 \sin(2t)+c\)

\(\dfrac{dS}{dt}=kS(5000-S)\)

\(\dfrac{dH}{dt}=\dfrac{kH(3000-H)}{t}\)

1. (a) \(s=-30e^{-\frac{t}{5}}+c\)
2. (b) 25.9 m

1. (a) \(F=5m + \frac{2}{m}+c\)
2. (b) \(G=t + 4e^{-2t}+c\)