Let be defined by the differential equation with

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

Problem

Let

y(x)

be defined by the differential equation

\dfrac{dy}{dx}=\dfrac{x^{2}}{y^{2}}

with

y(1)=2

. Which of the following gives

y

explicitly in terms of

x

? (a)

y(x)=\bigl(x^{3}-7\bigr)^{1/3}

(b)

y(x)=\bigl(3x^{2}+7\bigr)^{1/3}

(c)

y(x)=\bigl(x^{3}+7\bigr)^{1/3}

(d)

y(x)=\bigl(x^{3}+7\bigr)^{1/2}

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