1. Implement the Explicit Euler Scheme for Initial Value Problems of the form:    y'(t) = F(t, y(t)) , t0 ? t ? tend    y(t0) = y0  The function F(t,y) should be coded in a function subprogram FCN(...).  Input data: t0, y0, tend, Nsteps. Thus the time-step will be h=(tend-t0)/Nsteps.  Your code should print out the input data and then the pairs:        tn     Yn  At the end, it should print out the final n, tn, Yn  (appropriately labelled, of cource).2. Solve, on paper, the simple (integration) problem:        y' = 2t ,  0 ? t ? 1        y(0) = ?13. To debug your code, run it on the problem above.  Compare the numerical solution Yn with the exact solution yEXACT(tn),  i.e. modify your output to print out:    tn   Yn   yEXACTn     ERRn  where ERRn = |Yn - yEXACT(tn)|, and keep track of the maximum error.  At the end of the run, print out the above values (at time tend)  and the maximum overall error ERRmax. Test with N=10 and N=100.  Turn off printing of tn Yn ... and test with N = 1000, 10000 and larger.  Once the code is debugged, only FCN(...) and input data need to be changed  to solve other IVPs.4. Now solve the IVP:    y' = ?t/y ,  0 ? t ? 1    y(0) = 1  Find the exact solution at t = 1 (by hand),  and compare the numerical and exact values at t = 1.   Try small (N=10) and larger (N=100, 1000, 10000, ... ) number of time-steps.  At which time does the worst error occur in this problem ?  Plot the exact solution. Do you see why it occurs there?