9) A system is represented by a differential equation y' - xy + 3y = 62x with the boundary conditions y(1) = 1 and y(2) = 10. Find the response y from 0 to 2 with an increment h = 0.2.
b) The radial displacement pressure vessel across the thickness (inner radius a = 125mm, outer radius b = 200mm) follows a differential equation d^2u/dr^2 + (1/r) * du/dr + u/r^2 = 0.
In a condition of internal pressure, the displacement of inside (r = a) and outside (r = b) should be set as 0.0968275mm and 0.0769240mm respectively.
Illustrate the cross-section of the pressure vessel and the boundary condition of the displacement. Next, illustrate the 1-dimensional model of the thickness if divided by four nodes with the same distance (four equidistant nodes). Determine the radial displacement profile using the Finite Difference Method.