Given dy/dx = -200000y + 200000e^-x - e^-x a. verify that y = e^-x - e^-2000 00x is a solution for y(0) = 0. b. Estimate the step size required to maintain stability using the explicit Euler method. c. Why is this D.E. stiff? d. Verify (b) using software to solve the D.E. i. Use Euler's method -take several steps using h's that are less than, greater than, and equal to the value in (b). ii. Use a valid software option for stiff systems to solve from x = 0 to 0.1. Given dy/dx = -200000y + 200000e^-x - e^-x a. verify that y = e^-x - e^-2000 00x is a solution for y(0) = 0. b. Estimate the step size required to maintain stability using the explicit Euler method. c. Why is this D.E. stiff? d. Verify (b) using software to solve the D.E. i. Use Euler's method -take several steps using h's that are less than, greater than, and equal to the value in (b). ii. Use a valid software option for stiff systems to solve from x = 0 to 0.1