2. For this problem, we will consider a basic RL circuit consisting of one resistor, one inductor, and a voltage source in series. In this circuit, the current is governed by the differential equation dI # + RI = V where I is the current (in amperes), t is time (in milliseconds), L is the inductance (in millihenries), R is the resistance (in ohms), and V is the voltage. Note: I is a function of t, but R, L, and V are constants. (a) Solve for I(t) assuming that I(0) = 0. (b) Show that lim .x. I(!) = K. (c) Find to such that I(t) 2 1 75 whenever t 2 to- (d) Using the Desmos applet : https://www. desmos. com/calculator/z18twje8du, plot the different tial equation as well as the particular solution when L = 5 millihenries, R =5 ohms, and V = 10 volts. (i) Substitute the given values of L. R and V into the differential equation and into your solution from part (a). (ii) The applet requires that the differential equation is written as a function of r and y instead of t and I. Write the differential equation and solution using these variables. (iii) Attach a screenshot of your plot of the slope field overlaid with the plot of your solution. Be sure to also include your inputs on the left side in your screenshot. (iv) Explain in a sentence or two how the plot indicates that your solution to the differential equation is correct or incorrect