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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...

Question

(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.



Answers

Find the solution of the differential equation that satisfies the given initial condition.
$ x + 3y^2 \sqrt {x^2 + 1} \frac {dy}{dx} = 0, y(0) = 1 $


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