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What method would you use to solve:

$$ (1+x^2)\frac{\mathrm{d}y}{\mathrm{d}x}=1+y^2 \;; \qquad y(2)=3 $$

I am asking this because I only know two methods of solving the DEs - separation of variables and integrating factor. Since the separation of variables does not work here, I tried integrating factor, however, I don't know what to do with the $y^2$, because for the IF to work I need to get y on its own ($\frac{\mathrm{d}y}{\mathrm{d}x} + P(x)y = Q(x)$)

What method do I use to solve this?

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    $\begingroup$ I think that separation of variables works fine. $\endgroup$ – Claude Leibovici Feb 12 '15 at 12:24
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Why not separation? I get $$ \frac{1}{1+y^2} \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{1}{1+x^2} $$

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  • $\begingroup$ Oops, yes, something went wrong, lol $\endgroup$ – Badalyan Feb 12 '15 at 12:33

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