ODE
\[ \left (x^2+1\right ) y''(x)-x y'(x)+y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0301513 (sec), leaf count = 29
\[\left \{\left \{y(x)\to -c_2 \sqrt {x^2+1}+c_1 x+c_2 x \sinh ^{-1}(x)\right \}\right \}\]
Maple ✓
cpu = 0.038 (sec), leaf count = 23
\[ \left \{ y \left ( x \right ) =-\sqrt {{x}^{2}+1}{\it \_C2}+x \left ( {\it \_C2}\,{\it Arcsinh} \left ( x \right ) +{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[y[x] - x*y'[x] + (1 + x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] - Sqrt[1 + x^2]*C[2] + x*ArcSinh[x]*C[2]}}
Maple raw input
dsolve((x^2+1)*diff(diff(y(x),x),x)-x*diff(y(x),x)+y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = -(x^2+1)^(1/2)*_C2+x*(_C2*arcsinh(x)+_C1)