Question No. 3:

Part A: The most common use of differential equations in science is to model dynamical systems, i.e. systems that change in time according to some fixed rule. For such a system, the independent variable is t (for time) instead of x. For the following such ODE;

dydt=(3t2-y)2ty

Apply 4^th Order R-K Method with a step size of 0.2 to find the solution at t=1, where y= 1.2 at t=0.

Part B:

Develop a MATLAB code to solve the Differential Equation in Part-A using Euler Method. You may use Octave-online/MATLAB to develop and execute the code.