2022-085

Consider the following differential equation:

\( x y(x) = (1 + x^2) y'(x) \)

Which alternative represents a family of possible solutions?

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

Original Idea by Iury Cleveston