Hello

These are a math problems that need to solve by MATLAB as code

Thank you !

Initial Value Problem #1: Consider the following first order ODE: dy-p-3 from to 2.2 with y() I (a) Solve with Euler's explicit method using h04. (b) Solve with the midpoint method using h 0.4. (c) Solve with the classical fourth-order Runge-Kutta method using 0.4 analytical solution of the ODE is,? solution and the numerical solution at the points where the numerical solution is determined +In each part, calculate the error between the true Initial Value Problem #2: Consider the differential equation for mass-spring-damper system as shown: where k2 - 48 N/m/kg, y07s, x(0)0, and d0.2 m/s. Solve the ODE over the interva dt dx 031s5 s, and pla (two separate figures on one page) as a function of t. 1.) Write the second order ODE as a system of first order ODEs 2.) Solve for step size t = 0.1 seconds 3.) Provide brief discussion of the physics (derivation of governing equation) and explanation of the results