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Separable differential equations: find the error

AP.CALC: FUN‑7 (EU), FUN‑7.D (LO), FUN‑7.D.1 (EK), FUN‑7.D.2 (EK)

Problem

Kajal tried to solve the differential equation start fraction, d, y, divided by, d, x, end fraction, equals, minus, x, squared, y, squared. This is her work:
dydx=x2y2Step 1:y2dy=x2dxStep 2:y1=x33+CStep 3:y=3x3+C\begin{aligned} &&\dfrac{dy}{dx}&=-x^2y^2 \\\\ \text{Step 1:}&&\displaystyle\int -y^{-2}\,dy&=\displaystyle\int x^2\,dx \\\\ \text{Step 2:}&&y^{-1}&=\dfrac{x^3}{3}+C \\\\ \text{Step 3:}&&y&=\dfrac{3}{x^3}+C \end{aligned}
Is Kajal's work correct? If not, what is her mistake?
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