4.35.25 \(\left (x^2+1\right )^2 y''(x)+2 x \left (x^2+1\right ) y'(x)+y(x)=0\)

ODE
\[ \left (x^2+1\right )^2 y''(x)+2 x \left (x^2+1\right ) y'(x)+y(x)=0 \] ODE Classification

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Book solution method
TO DO

Mathematica
cpu = 0.0260597 (sec), leaf count = 22

\[\left \{\left \{y(x)\to \frac {c_2 x+c_1}{\sqrt {x^2+1}}\right \}\right \}\]

Maple
cpu = 0.009 (sec), leaf count = 17

\[ \left \{ y \left ( x \right ) ={({\it \_C1}\,x+{\it \_C2}){\frac {1}{\sqrt {{x}^{2}+1}}}} \right \} \] Mathematica raw input

DSolve[y[x] + 2*x*(1 + x^2)*y'[x] + (1 + x^2)^2*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (C[1] + x*C[2])/Sqrt[1 + x^2]}}

Maple raw input

dsolve((x^2+1)^2*diff(diff(y(x),x),x)+2*x*(x^2+1)*diff(y(x),x)+y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = (_C1*x+_C2)/(x^2+1)^(1/2)