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Problem Find the implicit general solution to the differential equation d y d x = x 2 1 − y 2 \displaystyle \frac{dy}{dx}=\dfrac{x^{2}}{\sqrt{1-y^{2}}} d x d y = 1 − y 2 x 2 y 1 − y 2 + arcsin y = x 3 3 + C \displaystyle y\sqrt{1-y^{2}}+\arcsin y=\frac{x^{3}}{3}+C y 1 − y 2 + arcsin y = 3 x 3 + C arcsin y = x 3 3 + C \displaystyle \arcsin y=\frac{x^{3}}{3}+C arcsin y = 3 x 3 + C 1 2 ( y 1 − y 2 + arcsin y ) = x 3 3 + C \displaystyle \frac{1}{2}\left(y\sqrt{1-y^{2}}+\arcsin y\right)=\frac{x^{3}}{3}+C 2 1 ( y 1 − y 2 + arcsin y ) = 3 x 3 + C 1 2 ( y 1 − y 2 + arcsin y ) = x 2 + C \displaystyle \frac{1}{2}\left(y\sqrt{1-y^{2}}+\arcsin y\right)=x^{2}+C 2 1 ( y 1 − y 2 + arcsin y ) = x 2 + C Browse the problem library