1. The problem statement, all variables and given/known data Cappy McGreenhorn is looking to buy a new MP3 player. His primary concern is the battery life of the MP3 player. He has decided on either the aPod or the bPod. The percentage of battery life A(t) (after t hours) for the aPod is governed by: (100 - t2)dA/dt + 4tA = 0; with A(0) = 100: The percentage of battery life B(t) (after t hours) for the bPod is governed by: 100dB/dt - B2 + 10000 = 0; with B(0) = 100 tanh(12): (a) Which MP3 player should Cappy buy in order to get the longest playback time? (b) What is the battery charge on the bPod at t = 6? (c) When does the aPod hold a 50% battery charge? 2. Relevant equations HINT: Do not use partial fractions to do the integration. Use the fact that: d/dx(arctanh(x)) =1/(1 - x2) 3. The attempt at a solution I worked out Apod to be (1/100) (100-t2)2 But I think this is wrong. The second part I used separable vales and ended up with B= 100tanh(1/100 (t + 12)) However, I know that my second solution must be wrong since you cannot have negative time and when the battery = 0, my time will be -12 hours. :( Is it possible to use integrating factors to do the first order ode problem for bpod?