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

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 = 0.01265 (sec), leaf count = 26

\[\left \{\left \{y(x)\to \frac {c_2 e^{\frac {x^2}{2}}-c_1}{x}\right \}\right \}\]

Maple
cpu = 0.098 (sec), leaf count = 18

\[ \left \{ y \left ( x \right ) ={\frac {1}{x} \left ( {\it \_C2}\,{{\rm e}^{{\frac {{x}^{2}}{2}}}}+{\it \_C1} \right ) } \right \} \] 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),'implicit')

Maple raw output

y(x) = (_C2*exp(1/2*x^2)+_C1)/x