40_pdfsam_math 54 differential equation solutions odd

40_pdfsam_math 54 differential equation solutions odd - t...

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Chapter 2 –4 –2 0 2 4 –2 2 a = 1 2 a =1 a =2 a = 1 2 a = 1 a = 2 Figure 2–A : Solutions to the initial value problem y 0 = xy 3 , y (0) = a , a ± 0 . 5, ± 1, and ± 2. (e) For the values a =1 / 2, 1, and 2 the solutions are found in (b); for a = 1, we just have to choose the negative sign in (2.6); similarly, we reverse signs in the other two solutions in (b) to obtain the answers for a = 1 / 2and 2. The graphs of these functions are shown in Figure 2-A. 33. Let A ( t ) be the number of kilograms of salt in the tank at
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Unformatted text preview: t minutes after the process begins. Then we have dA ( t ) dt = rate of salt in rate of salt out . rate of salt in = 10 L / min . 3 kg / L = 3 kg / min . Since the tank is kept uniformly mixed, A ( t ) / 400 is the mass of salt per liter that is owing out of the tank at time t . Thus we have rate of salt out = 10 L / min A ( t ) 400 kg / L = A ( t ) 40 kg / min . 36...
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