Problems 29 through 32 explore the connections among general and singular solutions, existence, and uniqueness (a) Find a general solution of the differential equation dy dx y 2 (b) Find a singular solution that is not included in the general solution (c) Inspect a sketch of typical solution curves to determine the points (a, b) for which the initial value problem y ' y 2 , y(a) b has a unique solution

Question: Problems 29 through 32 explore the connections among general and singular solutions, existence, and uniqueness. (a) Find a general solution of the differential equation dy/dx

Problems 29 through 32 explore the connections among general and singular solutions, existence, and uniqueness.

(a) Find a general solution of the differential equation dy/dx = y².

(b) Find a singular solution that is not included in the general solution.

(c) Inspect a sketch of typical solution curves to determine the points (a, b) for which the initial value problem y' = y², y(a) = b has a unique solution.

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