Which differential equation has the family of solutions

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Which differential equation has the family of solutions y=arcsin⁡x+Cy=\arcsin x + C, where CC is a constant? (a) −11−x2-\dfrac{1}{\sqrt{1-x^{2}}} (b) 11+x2\dfrac{1}{1+x^{2}} (c) 11−x2\dfrac{1}{\sqrt{1-x^{2}}} (d) 11−x2\dfrac{1}{1-x^{2}}

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