ODE
\[ x^3 \left (-y'(x)\right )+\left (1-x^2\right ) x^2 y''(x)-2 y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.198983 (sec), leaf count = 65
\[\left \{\left \{y(x)\to -\frac {\left (1-x^2\right )^{3/4} \left (-c_1 x^2+c_2 \sqrt {1-x^2} x+c_2 \left (x^2-1\right ) \sin ^{-1}(x)+c_1\right )}{x \left (x^2-1\right )^{5/4}}\right \}\right \}\]
Maple ✓
cpu = 0.252 (sec), leaf count = 61
\[\left [y \left (x \right ) = \frac {\textit {\_C1} \sqrt {x^{2}-1}}{x}+\frac {\textit {\_C2} \left (\left (x^{4}-2 x^{2}+1\right ) \ln \left (x +\sqrt {x^{2}-1}\right )-\left (x^{2}-1\right )^{\frac {3}{2}} x \right )}{\left (x^{2}-1\right )^{\frac {3}{2}} x}\right ]\] Mathematica raw input
DSolve[-2*y[x] - x^3*y'[x] + x^2*(1 - x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(((1 - x^2)^(3/4)*(C[1] - x^2*C[1] + x*Sqrt[1 - x^2]*C[2] + (-1 + x^2)*ArcSin[x]*C[2]))/(x*(-1 + x^2)^(5/4)))}}
Maple raw input
dsolve(x^2*(-x^2+1)*diff(diff(y(x),x),x)-x^3*diff(y(x),x)-2*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1/x*(x^2-1)^(1/2)+_C2/(x^2-1)^(3/2)/x*((x^4-2*x^2+1)*ln(x+(x^2-1)^(1/2))-(x^2-1)^(3/2)*x)]