Here are two methods for solving the differential equation dy = +1. = 1. dt 3' Jv'o a Solve the homogeneous equation :15 = y. Don't worry about the initial condition yet. Call the solution I . Note that of is also a solution. where a is any constant. Now. try a solution of the form of. where It is a function. Use the differential equation to determine what v has to be. a Let 2 = y + I. Use the differential equation dyldt = y + t to write a differential equation involving 2. which you can solve. Once you have 2. you can easily find y. I. Use either of the methods described to solve 6'? = t. = I. m y + 3'0 2. Con'pare your approximate solution from Part I with the exact solution. Describe the difference as precisely as you can. Explain the behavior of the approximation relative to the true solution. 3. Using the other method. solve 6'? E_2y+:v \"1. 4. Compare your solution with m approximate solution (as in Part 1). Describe the difference as precisely as you can. Explain the behavior of the approximaion relative to the true solution