Sketch the direction field of the differential equation. Then use it to sketch a solution curve that passes through the given point. 12. y' = xy - x2, (0, 1)24. (:1) Use Euler's method with step size 0.2 to estimate y(0.4), where y(x) is the solution of the initial-value problem y' =x + y2,y(0) = 0. (b) Repeat part (a) with step size 0.1. 23. In Exercise 14 in Section 7.1 we considered a 95C cup of cof- fee in a 20C room. Suppose it is known that the coffee cools at a rate of 1C per minute when its temperature is 70C. (a) What does the di'erential equation become in this case? (b) Sketch a direction eld and use it to sketch the solution curve for the initial-value problem. What is the limiting value of the temperature? (c) Use Euler's method with step size it = 2 minutes to estimate the temperature of the coffee after 10 minutes