Consider subject to the initial condition dy da = y lnx y (1) = 1 1. Numerically solve the equation for x = [1,2] using Euler's method with (a) h = 0.1. (b) h = 0.05. 2. Find an exact solution to the equation using separation of variables. 3. Using your exact solution, find the relative percent error for your numerical approximations of y(2). 4. Plot all three solutions on one graph, clearly labeling each curve. Consider subject to the initial condition dy da = y lnx y (1) = 1 1. Numerically solve the equation for x = [1,2] using Euler's method with (a) h = 0.1. (b) h = 0.05. 2. Find an exact solution to the equation using separation of variables. 3. Using your exact solution, find the relative percent error for your numerical approximations of y(2). 4. Plot all three solutions on one graph, clearly labeling each curve.