6. [3 points] Consider the following differential equation for o(r), d³o do +14 - 80 = 1, dt (7) dt² with the following conditions, o(0) = 0, (0) = 1, and

"(0) = 1. (a) [1 points] Convert the above differential equation into a system of coupled first-order differential equations. Clearly identify your new variables (b) [1 points] Clearly identify the conditions for the new variables for this system of differ- ential equations. (c) [1 point] Write down the finite difference approximation for each equation using the forward Euler method. Clearly identify the notation you are using. Your approximation should be based on knowing the solution at t, and predicting solution at t+1.