Marks Consider the following differential equation: dy with the initial condition y(0) = 1. V2y 1+0.50 dt a) Find the value of y when t = 2 using Euler's method, using a step size of 0.1. B 1 U X x? ABC 123 y value at t = 2 using Euler's method = [4dp] b) Find the value of y when t = 2 using Heun's method, using a step size of 0.1. i B I U X2 x? = = ABC 123 5 c. y value when t = 2 using Heun's method = [4dp] d) Write a Matlab code to perform the following: dy Define dt Define a vector with step sizes 1,0.5,0.1,0.01s - Pre-allocate a vector named y_t2 that has the same dimensions as the vector with step sizes. Use Heun's method to determine the y value at t 2, for each step size. Use a for loop. Store the results in the y_t2 vector corresponding to each step size. i B I U X2 x2 = = = III ll IM ABC 123 Copy and paste your Matlab code here