Discuss direction fields as follows.(a) Graph portions of the direction field of the ODE (2) (see Fig. 7), for instance, -5<x<2, -1<y<5. Explain what you have gained by this enlargement of the portion of the field.(b) Using implicit differentiation, find an ODE with the general solution x²+ 9y²= c (y > 0).^?Graph its direction field. Does the field give the impression that the solution curves may be semi-ellipses? Can you do similar work for circles? Hyperbolas? Parabolas? Other curves?(c) Make a conjecture about the solutions of y' = -x/y from the direction field.(d) Graph the direction field of y' = -1/2y and some solutions of your choice. How do they behave? Why do they decrease for y > 0?

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م هر هر هر همر هر هر جس هرجاس -2-1.5 -1-0.5 -0.5 1 x می هر هر هی ه = 1. Fig. 7. Direction field of y' = y + x, with three approximate solution curves passing through (0, 1), (0, 0), (0, –1), respectively S 1 11 11t t