Linear Second Order ODE/(1 + x^2) y'' + x y' = 0

Theorem
The second order ODE:
 * $\left({1 + x^2}\right) y'' + x y' = 0$

has the solution:
 * $y = C_1 \ln \left({x + \sqrt {x^2 + 1} }\right) + C_2$

Proof
The proof proceeds by using Solution of Second Order Differential Equation with Missing Dependent Variable.

Substitute $p$ for $y'$: