Taylor's series method to solve first order first degree ODE

Consider the initial value problem given by the ODE dy dt = y − t 2 + 1, y(0) = 0.5. a. Use the Taylor Series Method (up to the second order) to derive the Taylor series expansion for the solution of the ODE around t = 0. Calculate the first few terms of the series. b. Implement the Taylor Series Method in MATLAB to approximate the solution over the interval t = [0, 2] and plot the result. c. Use the Second and Fourth-Order Runge-Kutta method to numerically solve the same ODE over the interval t = [0, 2] and plot solutions on the same graph as the Taylor Series approx- imation. d. Compare the three numerical methods based on their accuracy and computational efficiency, and discuss scenarios where one method may be preferred over the other.