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Solutions Manual for Applied Numerical Methods with Python for Engineers and Scientists by Steven C. Chapra, David Clough

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Solution Manual for Applied Numerical Methods with Python for Engineers and Scientists by Steven C. Chapra, David Clough #Chapter 1 1.1 Use calculus to verify that Eq. (1.9) is a solution of Eq. ( ... 1.8) for the initial condition v(0) = 0. ========================================== You are given the following differential equation with the initial condition, v(0) = 0, dv cd 2 g v dt m = − Multiply both sides by m/cd 2 d d m dv m g v c dt c = − Define / d a mg c = 2 2 d m dv a v c dt = − Integrate by separation of variables, 2 2 d dv c dt a v m = −   A table of integrals can be consulted to find that 1 2 2 1 tanh dx x a x a a − = −  Therefore, the integration yields 1 1 tanh d v c t C a a m − = + If v = 0 at t = 0, then because tanh–1 (0) = 0, the constant of integration C = 0 and the solution is 1 1 tanh d v c t a a m − = This result can then be rearranged to y [Show More]

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