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Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (x0,y0) in the region. (9 - y^2)y' = x^2 (1) A unique solution exists in the entire xy-plane. (2) A unique solution exists in the region consisting of all points in the xy-plane except (0, 3) and (0, -3). (3) A unique solution exists in the region y > -3. (4) A unique solution exists in the region y < 3. (5) A unique solution exists in the regions y < -3, -3 < y < 3, and y > 3.

Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (x0,y0) in the region. (9 - y^2)y' = x^2 (1) A unique solution exists in the entire xy-plane. (2) A unique solution exists in the region consisting of all points in the xy-plane except (0, 3) and (0, -3). (3) A unique solution exists in the region y > -3. (4) A unique solution exists in the region y < 3. (5) A unique solution exists in the regions y < -3, -3 < y < 3, and y > 3.

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Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (x0,y0) in the region. (9 - y^2)y' = x^2 (1) A unique solution exists in the entire xy-plane. (2) A unique solution exists in the region consisting of all points in the xy-plane except (0, 3) and (0, -3). (3) A unique solution exists in the region y > -3. (4) A unique solution exists in the region y < 3. (5) A unique solution exists in the regions y < -3, -3 < y < 3, and y > 3.

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