The function satisfies and

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

Problem

The function

y=f(x)

satisfies

\displaystyle \frac{dy}{dx}=\frac{x}{1+y^{2}}

and

f(0)=1

. Which of the following is an implicit equation for the particular solution? (a)

y+\dfrac{y^{3}}{3}=\dfrac{x^{2}}{2}-\dfrac{4}{3}

(b)

\arctan y=\dfrac{x^{2}}{2}+1

(c)

y+\dfrac{y^{3}}{3}=\dfrac{x^{2}}{2}+\dfrac{4}{3}

(d)

y+\dfrac{y^{3}}{3}=x^{2}+\dfrac{4}{3}

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