<s>[INST] Simple first order differential equation I've got another first order differential that has me stumped.  Please see my work and let me know where I'm going wrong:
$$y' = \frac{6x^2}{y(1+x^3)}$$
$$y'y = \frac{6x^2}{1+x^3}$$
$$ y.\frac{dy}{ dx} = \frac{6x^2}{1+x^3} $$
$$\int y dy = \int 6x^2\frac{1}{1+x^3} dx$$
$$\frac{1}{2}y^2 = 2x^3 \ln|1 + x^3| + c$$
$$y^2 = 4x^3 \ln|1 + x^3| + c$$
$$y = \pm \sqrt{4x^3 \ln |1 + x^3| + c}$$
Unfortunately, my answer is wrong and I'm not quite sure why.  Please help.
 [/INST] Your error is that $\displaystyle\int\dfrac{6x^2}{1+x^3}\,dx = 2\ln|1+x^3|+C$ and not $2x^3\ln|1+x^3|+C$. 
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