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(a) Solve the differential equation $y^{\prime}=2 x \sqrt{1-y^{2}}$. (b) Solve the initial-value problem $y^{\prime}=2 x \sqrt{1-y^{2}}$, $y(0)=0$, and graph the so...

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(a) Solve the differential equation $y^{\prime}=2 x \sqrt{1-y^{2}}$. (b) Solve the initial-value problem $y^{\prime}=2 x \sqrt{1-y^{2}}$, $y(0)=0$, and graph the solution. (c) Does the initial-value problem $y^{\prime}=2 x \sqrt{1-y^{2}}$, $y(0)=2$, have a solution? Explain.

(a) Solve the differential equation $y^{\prime}=2 x \sqrt{1-y^{2}}$. (b) Solve the initial-value problem $y^{\prime}=2 x \sqrt{1-y^{2}}$, $y(0)=0$, and graph the solution. (c) Does the initial-value problem $y^{\prime}=2 x \sqrt{1-y^{2}}$, $y(0)=2$, have a solution? Explain.

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