Work Sheet Assignment 15: Consider IVPs dx/dt = -5t x, x(0) = xo > 0 R_, t > 0 where a > -1. Implement the outer Theta methods (OTMs) depending on parameter 6 [0, 1] on your computer, while using constant (equidistant) step sizes h > 0. You may use packages like MAPLE, MATHEMATICA, MATLAB or languages R, C, PYTHON. Fix initial value Xo = 1.0. Consider the instantaneous error e(tn, a, 0,h) := |x(tn, a) yn(a,0, h)]. (a) Solve this IVP analytically. (b) Fix initial value Xo = 1.0. Plot the error e(tn, a, 0, h) in 3D, as function depending on tn (0, 2) and h (0.001,0.1), while a = 3 and 0 = 0,0.5, 1 are fixed. (c) Fix initial value Xo = 1.0. Plot the error e(tn, a, 0, h) in 3D, as function depending on a (-1,3] and h (0.001,0.1), while T = 2 = tend = ty and 0 = 0,0.5, 1 are fixed. (d) Fix initial value Xo = 1.0. Plot the error e(tn,a,0,h) in 3D, as function depending on 0 (0, 1) and h (0.001,0.1), while T = 2 = tend = ty and a = 1, 2, 3 are fixed. Describe your major observations in items (b)-(d). Provide all 3D pictures (9 total from items (b)-(d)) at the end of your pdf file of WSA3 response. Work Sheet Assignment 15: Consider IVPs dx/dt = -5t x, x(0) = xo > 0 R_, t > 0 where a > -1. Implement the outer Theta methods (OTMs) depending on parameter 6 [0, 1] on your computer, while using constant (equidistant) step sizes h > 0. You may use packages like MAPLE, MATHEMATICA, MATLAB or languages R, C, PYTHON. Fix initial value Xo = 1.0. Consider the instantaneous error e(tn, a, 0,h) := |x(tn, a) yn(a,0, h)]. (a) Solve this IVP analytically. (b) Fix initial value Xo = 1.0. Plot the error e(tn, a, 0, h) in 3D, as function depending on tn (0, 2) and h (0.001,0.1), while a = 3 and 0 = 0,0.5, 1 are fixed. (c) Fix initial value Xo = 1.0. Plot the error e(tn, a, 0, h) in 3D, as function depending on a (-1,3] and h (0.001,0.1), while T = 2 = tend = ty and 0 = 0,0.5, 1 are fixed. (d) Fix initial value Xo = 1.0. Plot the error e(tn,a,0,h) in 3D, as function depending on 0 (0, 1) and h (0.001,0.1), while T = 2 = tend = ty and a = 1, 2, 3 are fixed. Describe your major observations in items (b)-(d). Provide all 3D pictures (9 total from items (b)-(d)) at the end of your pdf file of WSA3 response