Trying to solve this First Order Differential Equation. I've made several attempts to this question but they've been unsuccessful. The question is shown below:
$$(1+x^2)\frac{\text{d}x}{\text{d}y}+xy=0$$
the answer in the book states when y(0)=2 
$$y^2(1+x^2)=4$$ however I gain $c^2=y^2(1+x^2)$ and when the boundary condition is applied this answer is not achieved 

It looks like you're correct - for $x=0$ and $y=2$, we have $c^2 = 2^2 (1 + 0^2)$, so $c^2 = 4$. So, your equation becomes $y^2 (1+x^2) = c^2 = 4$, as required.
