ODE
\[ x^2 y''(x)+\left (1-x^2\right ) x y'(x)-\left (x^2+1\right ) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.173873 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \frac {c_2 e^{\frac {x^2}{2}}-c_1}{x}\right \}\right \}\]
Maple ✓
cpu = 0.067 (sec), leaf count = 21
\[\left [y \left (x \right ) = \frac {\textit {\_C1}}{x}+\frac {\textit {\_C2} \,{\mathrm e}^{\frac {x^{2}}{2}}}{x}\right ]\] Mathematica raw input
DSolve[-((1 + x^2)*y[x]) + x*(1 - x^2)*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-C[1] + E^(x^2/2)*C[2])/x}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+x*(-x^2+1)*diff(y(x),x)-(x^2+1)*y(x) = 0, y(x))
Maple raw output
[y(x) = 1/x*_C1+_C2/x*exp(1/2*x^2)]