Find the implicit general solution to the differential equation .

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Find the implicit general solution to the differential equation dydx=x21−y2\displaystyle \frac{dy}{dx}=\dfrac{x^{2}}{\sqrt{1-y^{2}}}. (a) y1−y2+arcsin⁡y=x33+C\displaystyle y\sqrt{1-y^{2}}+\arcsin y=\frac{x^{3}}{3}+C (b) arcsin⁡y=x33+C\displaystyle \arcsin y=\frac{x^{3}}{3}+C (c) 12(y1−y2+arcsin⁡y)=x33+C\displaystyle \frac{1}{2}\left(y\sqrt{1-y^{2}}+\arcsin y\right)=\frac{x^{3}}{3}+C (d) 12(y1−y2+arcsin⁡y)=x2+C\displaystyle \frac{1}{2}\left(y\sqrt{1-y^{2}}+\arcsin y\right)=x^{2}+C

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