Consider the differential equation dy/dt = t y. (a) Sketch the slope field of the differential

Consider the differential equation dy/dt = t − y.

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(a) Sketch the slope field of the differential equation =ty in the range -1 ≤ ≤ 3, -1 ≤ y ≤ 3. As an dy dt aid, observe that the isocline of slope c is the line t - y = c, so the segments have slope c at points on the line y = t - c. 1-00 (b) Show that y = t - 1 + Ce is a solution for all C. Since lim e = 0, these solutions approach the particular solution y = t - 1 as t→ ∞o. Explain how this behavior is reflected in your slope field.