Problem 1: Euler's Method (Basic)Use Euler's Method to approximate the solution of the initial value problem:dydx=x+y,y(0)=1Find the approximate values ofyatx=0.1,0.2,0.3 using a step size h=0.1.Problem 2: Modified Euler's MethodUse the Modified Euler's Method to solve the same initial value problem:dydx=x+y,y(0)=1Use a step size h=0.1h=0.1h=0.1to approximate yatx=0.1,0.2,0.3. Compare the results withthose obtained from Euler's Method in Problem 1.Problem 3: Error ComparisonThe exact solution of the ODE dydx=x+y,y(0)=1is:y(x)=2ex-x-1Calculate the exact values ofyatx=0.1,0.2,0.3.Compute the absolute error for both Euler's and Modified Euler's methods.Discuss which method gives better approximation and why.