(Solution) - a What can you say about the several members of the -(2025 Original AI-Free Solution)

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Academic Level: Undergrad. (yrs 3-4)

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(a) What can you say about the graph of a solution of the equation y? = xy3 when is close to 0? What if is large?
(b) Verify that all members of the family y = (c ? x2)?½ are solutions of the differential equation y? = xy3.
(c) Graph several members of the family of solutions on a common screen. Do the graphs confirm what you predicted in part (a)?
(d) Find a solution of the initial-value problem y? = xy3 y (0) = 2