By hand, apply Euler’s method with n = 3 steps to solve the initial value problem, x˙ = x 2 /4, x(0) = 2, up to terminal time t = 3/2. You may use a calculator if you like, but show each line as the algorithm progresses. What is the actual error in your solution at terminal time, t = 3/2? Note that the true solution has the form ¯x(t) = −1/(c + t/4) for some value of c < 0 (that we’ll let you find), and obviously would go off to infinity as t ↑ −4c. Because of that, you might not expect the numerical method to perform well with so few steps.