Use the RungeKutta method with step size h 005 to approxima

Use the Runge-Kutta method with step size h = 0.05 to approximate to three decimal places the values of the following differential equation on the given interval with the given initial condition dv/dt = 32 -1.6t v(0) =0, o lessthanorequalto t lessthanorequalto 1 Find the exact solution and make (print in Microsoft Word) a table showing the approximate and the exact solution.

Solution

Want to solve y\' = f(x,y) with y(x0) = y0 Runge-Kutta Method x0 = 0 y0 = 0 h= 0.05 n x(n) y(n) k1 k2 k3 k4 y(n+1) = y(n)+(h/6)*(k1 + 2*k2 + 2*k3 + k4) 0 0 0 32 31.96 31.96 31.92 1.598 1 0.05 1.598 31.92 31.88 31.88 31.84 3.192 2 0.1 3.192 31.84 31.8 31.8 31.76 4.782 3 0.15 4.782 31.76 31.72 31.72 31.68 6.368 4 0.2 6.368 31.68 31.64 31.64 31.6 7.95 5 0.25 7.95 31.6 31.56 31.56 31.52 9.528 6 0.3 9.528 31.52 31.48 31.48 31.44 11.102 7 0.35 11.102 31.44 31.4 31.4 31.36 12.672 8 0.4 12.672 31.36 31.32 31.32 31.28 14.238 9 0.45 14.238 31.28 31.24 31.24 31.2 15.8 10 0.5 15.8 31.2 31.16 31.16 31.12 17.358 11 0.55 17.358 31.12 31.08 31.08 31.04 18.912 12 0.6 18.912 31.04 31 31 30.96 20.462 13 0.65 20.462 30.96 30.92 30.92 30.88 22.008 14 0.7 22.008 30.88 30.84 30.84 30.8 23.55 15 0.75 23.55 30.8 30.76 30.76 30.72 25.088 16 0.8 25.088 30.72 30.68 30.68 30.64 26.622 17 0.85 26.622 30.64 30.6 30.6 30.56 28.152 18 0.9 28.152 30.56 30.52 30.52 30.48 29.678 19 0.95 29.678 30.48 30.44 30.44 30.4 31.2 20 1 31.2 30.4 30.36 30.36 30.32 32.718 value 31.2