1. Solve the following initial value problem dy = x + y, dx y(0) = 1 %3D by the Euler Method and Heun's method to estimate y (0.1) using h = 0.05. Also estimate the percentage error of the numerical...

Extracted text: 1. Solve the following initial value problem dy = x + y, dx y(0) = 1 %3D by the Euler Method and Heun's method to estimate y (0.1) using h = 0.05. Also estimate the percentage error of the numerical result with the exact answer given by the analytical solution as: y(x) = 3e* – x - 2x – 2. 2. An object with a mass, m= 10 kg is falling under the influence of earth gravity. The object starts from rest and experiences a retarding force equal to 0.25 of its velocity, v, i.e., in differential equation form, dy 2 = x* + y, dx y(0) = 1 Find its velocity, v after time, t = 4 seconds using the classical 4th order R-K method with a step size, h = 2 seconds. Solve it analytically and determine the percentage error of your numerical estimate. [g = 9.81 m/s²]