21 a) Find the general solution to the homogeneous second-order linear ordinary differential equation d² y dx² + 3 dy dx - 4y = 0. [5 marks] b) Find the solution to the Initial value Problem of the second-order ODE in part a) with the initial Conditions y(0) = 5, y'(0) = 0. [5 marks] c) Now transform the Second order ODE of an independent variable x in part a), i.e. d²y + 3 ay dx 2 dx -4y=0, to a dynamical System of first-order ODEs of the independent variable as time t. [8 marks] d) Find the corresponding eigenvalues and eigenvectors of the transformed dynamical ODE System in part c) and write down its general solution. Compare this general solution with the general solution obtained in part a) and explain why they are equivalent through the transformation in part c). [12 marks]