18 [A comparison of methods] The alternative method for drawing the slope eld presented in the previous question is impractical when the expression for y' is a complicated or an unknown curve. In some instances, however, it is much preferable. Consider the differential equation y' = . a i ii iii iv ii iii iv x ). What can be said about the line elements of the slope eld for points on the y-axis other than the origin? The value of y' at points on the x-axis is undened. By considering lim v' and lim v' when x 74$ 0, }'.D* ' vo0' ' what can be said about the line elements of the slope eld for points on the x-axis? Draw the slope eld using a grid of points as in Questions 2 and 3 or by using software such as the free internet application WolframAlpha. What shape seems to be suggested? What is the equation of the isocline corresponding to y' = C? On a new number plane, draw by hand the isoclines for C = i; 1%, \\/ 3 and \\/ 3. (Hint: What angles of inclination correspond to these gradients?) Explain why each line element is perpendicular to its isocline. Add line elements to each isocline at equally spaced intervals. Is the shape of part c clearer now