Using python Solve the following equation numerically using the Heun method using h=0.1 and 0≤ t ≤10 du dt = (5t 2−u ) e (x +y) with the initial condition at t=0 , u (0)=1 As part of the solution process, converge the solution by decreasing the step size h. To determine if the solution is converged, you can find the maximum u (t ) for each step size h and plot maximum u (t ) .vs decreasing stepsize h.

(Statics) An annulus is a cylindrical rod with a hollow center, as shown in Figure 6.7. Its second moment of inertia is given by this formula: I4(r24r14) I is the second moment of inertia (m4). r2 is the outer radius (m). r1 is the inner radius (m). a. Using this formula, write a function called annulusMoment ( ) that accepts two double-precision numbers as parameters (one for the outer radius and one for the inner radius), calculates the corresponding second moment of inertia, and displays the result. b. Include the function written in Exercise 5a in a working program. Make sure your function is called from main(). Test the function by passing various data to it.