For the given initial value problem y' = 3xex - y(1 - 1/x), x0 = 1, y0 = 0, X = 5 realize:
by using your favorite programming language (Python) in your own software application.
Realize the exact solution of an IVP in your application.
Using this application, construct corresponding approximation of the solution of a given initial value problem.
Provide data visualization capability (graphs plotting) in the user interface of your application for ploting the graphs of exact and numerical solutions.
Investigate the convergence of these numerical methods on different grid sizes.
Compare approximation errors of these methods plotting the corresponding chart for different grid sizes.
Provide the possibility to change initial conditions x0, y0, grid size X, range of grid steps h.
Implementation should obey to OOP-design standards, in particular, the code should be organized within SOLID principles (especially within single responsibility principle, Liskov substitution principle, interface segregation principle).
Write a PDF-report (5-7 pages), containing your exact solution, source code and screenshots of numerical investigations, analysis of points of discontinuity, if exists, UML-diagram of classes and the most interesting parts of source code.