2022-085

Consider the following differential equation:

$xy(x)=(1+x^2)y^{\prime }(x)$

Which alternative represents a family of possible solutions?

1. $y(x)=c\sqrt{e^x+1}$
2. $y(x)=ce(x^2+1)$
3. $y(x)=c\sqrt{x^2+1}$
4. $y(x)=ce(x-1)$
5. None of the above

Original Idea by Iury Cleveston