In C++

DC Write a program that calculates the capacitor voltage after the switch is closed. The capac- itor is initially uncharged. Perform the simulation for a duration of five seconds. Use Vpc 0.5 volts Steps: i) Write the differential equation for the circuit after the switch is closed. The equation should be in terms of R, C, Ve, and Vpc i) Approximate the differential equation with a finite difference equation. Use the first order forward difference equation dt stepsize to approximate the derivative. Numerically solve the above difference equation for Vdi+1) iii) Write a C program that iterates the difference equation and prints out the voltage at each time instant. Analysis: a) Use a simulation time step of 0.1 seconds. Use the following values of R and C a) R 10,000 ohms, C 0.0002F b) R= 5,000 ohms, C=0.000 IF b) Use a simulation time step of 0.5 seconds. Use the following values of R and C a) R 10,000 ohms, C- 0.0002F b) R= 5,000 ohms, C 0.0001 F