A curve satisfies and passes through

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A curve satisfies dydx=x2y\dfrac{dy}{dx}=\dfrac{x}{2y} and passes through (0,1)(0,1). Which of the following is its equation? (a) y2=x2+1y^{2}=x^{2}+1 (b) y2=x22+1y^{2}=\dfrac{x^{2}}{2}+1 (c) y2=x24+1y^{2}=\dfrac{x^{2}}{4}+1 (d) y2=x22−1y^{2}=\dfrac{x^{2}}{2}-1

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