AT&T 3:09 PM (a) Sketch the slope field of the differential equation dt = ty = t y in the l S y S 3. As an aid, observe that the isocline of range 1 s. t S 3, slope c is the line t y = c, so the segments have slope c at points on the line y = t c. (b) Show that y = t 1 + Cet is a solution for all C. Since lim 00 O, these solutions approach the particular solution y = t 1 00. Explain how this behavior is reflected in your slope field. 6. how that the isoclines of = 1 / y are horizontal lines. Sketch the slope field for 2 S t S 2, 2 S y S 2 and plot the solutions with initial conditions y(O) = O and y(O) = 1. dy 7. Sketch the slope field for dt dy 8. Sketch the slope field for 9. Show that the isoclines of = t are vertical lines. Sketch the slope dt field for 2 S t 2, 2 S y 2 and plot the integral curves passing through (O, 1) and (C), 1). dy 10. ketch the slope field of = ty for 2 S t 2, 2 S y 2. dt Based on the sketch, determine lim y(t), where y(t) is a solution with y(O) > O. What is lim y(t) if y(O) < O? 11. Match each differential equation with its slope field in Figures dy dt dy (iii) dt 2 (ii) dt (vi) = t dt 2 Y 1/6