# Runge-Kutta 4

1. If air resistance is proportional to the square of the instantaneous velocity, then the velocity v of a mass m dropped from a given height is determined from:

m*dv/dt = mg - kv^, k>0.

Let: v(0) = 0, k = 0.125, m = 5 slugs, and g = 32 ft/s^2

a) Use a fourth-order Runge-kutta (RK4) method with h = 1 to approximate the velocity v(5)

b) Use excel to graph the solution of the IVP on the interval [0,6].

c) Use separation of variables to solve the IVP and then find the actual value.

2. Find the analytic solution of the initial-value problem (IVP)

y' = -y +10sin(3x), y(0) = 0, on the interval [0,2].

a) Graph the solution and find its positive roots.

b) Use Runge-Kutta (RK4) method with h = 0,1 to approximate a solution of the initial-value problem (IVP)

https://brainmass.com/math/ordinary-differential-equations/runge-kutta-method-problem-574440

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The solution shows in a step by step manner how to solve a first order differential equation using order 4 Runge-Kutta method and comparing it to the analytic solution