Show transcribed image text A simple method of integrating an ODE in state space form is called Euler's method. This method is a first order method that often has sufficient accuracy for many problems. If you have a nonlinear differential equation in vector form as x.(t) = f(x(t), u(t)), x(0) = x0 the equation can be approximately integrated using the following equation x(t + Delta t) = x(t) + Delta t f(x(t), u(t)) where Delta t is the integration time step and x(t + Delta t) is the solution for the system state vector at t + Delta t. If the time step is small enough, the numerical solution can be made arbitrarily close to the true solution. Use Euler's method to integrate the state space representation derived in problem 2 assuming that the initial condition of your state space representation is zero and the control input is u(t) = (t). Then compute the analytical solution for x(t) using the control input u(t) = 1(t) and show the for small enough time step the Euler solution agrees with your analytical solution.