Python language

Exercise E.1: Solve a simple ODE with function-based code This exercise aims to solve the ODE problem u - 10u' = 0, u(0) = 0.2, forte [0,20] a) Identify the mathematical function f(u,t) in the generic ODE form u = f(u,t). b) Implement the f(u, t) function in a Python function. c) Use the ForwardEuler function from Section E.1.3 to compute a numerical solution of the ODE problem. Use a time step At = 5. d) Plot the numerical solution and the exact solution u(t) = 0.2e-0.16 e) Save the numerical solution to file. Decide upon a suitable file format f) Perform simulations for smaller At values and demonstrate visually that the numerical solution approaches the exact solution