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 = 0.0892921 (sec), leaf count = 65
\[\left \{\left \{y(x)\to \frac {\sqrt [4]{1-x^2} \left (c_1 \sqrt {1-x^2}-c_2 \sqrt {1-x^2} \sin ^{-1}(x)+c_2 x\right )}{x \sqrt [4]{x^2-1}}\right \}\right \}\]
Maple ✓
cpu = 0.109 (sec), leaf count = 61
\[ \left \{ y \left ( x \right ) ={\frac {1}{x} \left ( {\it \_C2}\, \left ( -1+x \right ) ^{2} \left ( 1+x \right ) ^{2}\ln \left ( x+\sqrt {{x}^{2}-1} \right ) - \left ( {x}^{2}-1 \right ) ^{{\frac {3}{2}}}{\it \_C2}\,x+ \left ( -1+x \right ) ^{2} \left ( 1+x \right ) ^{2}{\it \_C1} \right ) \left ( {x}^{2}-1 \right ) ^{-{\frac {3}{2}}}} \right \} \] 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)^(1/4)*(Sqrt[1 - x^2]*C[1] + x*C[2] - Sqrt[1 - x^2]*ArcSin[x]*C[2]))/(x*(-1 + x^2)^(1/4))}}
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),'implicit')
Maple raw output
y(x) = 1/(x^2-1)^(3/2)*(_C2*(-1+x)^2*(1+x)^2*ln(x+(x^2-1)^(1/2))-(x^2-1)^(3/2)*_C2*x+(-1+x)^2*(1+x)^2*_C1)/x