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        Results for the Running Homework Problem

                y'   =  5*sin(2x) - y
                y(0) =  -1

        on interval [0, 1] using nodes of stepsize h = 0.2.

        x0 =   0.0000
        y0 =  -1.0000
        h  =   0.2000



                 | Exact Soln |    EXPLICIT EULER    |    IMPLICIT EULER
      n     x    |   y*(x)    |      y       Error   |      y       Error
    -------------+------------+----------------------+---------------------
      0   0.000  |  -1.00000  |  -1.00000            |  -1.00000
      1   0.200  |  -0.63397  |  -0.80000   0.16603  |  -0.50882  -0.12515
      2   0.400  |  -0.00574  |  -0.25058   0.24484  |   0.17378  -0.17952
      3   0.600  |   0.75614  |   0.51689   0.23924  |   0.92152  -0.16538
      4   0.800  |   1.50730  |   1.34555   0.16175  |   1.60091  -0.09361
      5   1.000  |   2.10947  |   2.07601   0.03346  |   2.09184   0.01763
                                            



                 | Exact Soln |  TRAPEZOIDAL MTHD    |    MODIFIED EULER    |  Classical Runge-Kutta
      n     x    |   y*(x)    |      y       Error   |      y       Error   |      y        Error
    -------------+------------+----------------------+----------------------+-------------------------
      0   0.000  |  -1.00000  |  -1.00000            |  -1.00000            |  -1.00000
      1   0.200  |  -0.63397  |  -0.64117   0.00720  |  -0.62529  -0.00868  |  -0.63397  -6.4459e-06
      2   0.400  |  -0.00574  |  -0.02152   0.01578  |   0.00171  -0.00744  |  -0.00573  -5.4944e-06
      3   0.600  |   0.75614  |   0.73212   0.02402  |   0.75436   0.00177  |   0.75613   1.1296e-06
      4   0.800  |   1.50730  |   1.47701   0.03029  |   1.49118   0.01612  |   1.50729   1.1167e-05
      5   1.000  |   2.10947  |   2.07613   0.03334  |   2.07724   0.03223  |   2.10945   2.2101e-05