Let y(t) be the solution to dy/dt = te^−y satisfying y(0) = 0.
(a) Use Euler’s Method with time step h = 0.1 to approximate y(0.1), y(0.2), . . . , y(0.5).
(b) Use Separation of Variables to find y(t) exactly.
(c) Compute the errors in the approximations to y(0.1) and y(0.5).