Please provide solution to all parts in detailed steps as per requirements set out in red fonts. I will upvote and give excellent review if your solution makes sense.

Question 4: [55 marks] a) Determine whether the differential equation y' 2y In x = X -is linear or nonlinear? - separable or non-separable? - homogeneous or non-homogeneous? Give reason to your answers. b) Find a general solution and then, a particular solution subject to the initial condition y(1) = 1. c) Determine whether the solution is the odd or even function? d) Verify the solution obtained by its substitution into the original equation. e) Using a technology (for example, a Matlab), plot the solution in the interval x e [1, 10]. Rubric: 5 marks if equation type was determined correctly; 15 marks if the general solution was found correctly; 2 marks if a constant of integration was included; 2 marks if the constant of integration was correctly determined from the initial condition; 3 marks if the final solution subject to the initial condition was presented in the correct form; 5 marks if function parity (evenness) was determined correctly; 15 marks if solution was correctly validated; 8 marks if solution is correctly presented graphically