ODE
\[ x^4 y''(x)-\left (1-x^2\right ) x y'(x)+\left (1-x^2\right ) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0266868 (sec), leaf count = 22
\[\left \{\left \{y(x)\to x \left (c_2 e^{-\frac {1}{2 x^2}}+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.059 (sec), leaf count = 16
\[ \left \{ y \left ( x \right ) =x \left ( {{\rm e}^{-{\frac {1}{2\,{x}^{2}}}}}{\it \_C2}+{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[(1 - x^2)*y[x] - x*(1 - x^2)*y'[x] + x^4*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*(C[1] + C[2]/E^(1/(2*x^2)))}}
Maple raw input
dsolve(x^4*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) = x*(exp(-1/2/x^2)*_C2+_C1)