ODE
\[ x^3+\left (1-x^2\right ) x y''(x)-y'(x)=0 \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0211616 (sec), leaf count = 30
\[\left \{\left \{y(x)\to -c_1 \sqrt {1-x^2}+c_2+\frac {x^2}{2}\right \}\right \}\]
Maple ✓
cpu = 0.041 (sec), leaf count = 23
\[ \left \{ y \left ( x \right ) ={\frac {{x}^{2}}{2}}+\sqrt {-1+x}\sqrt {1+x}{\it \_C1}+{\it \_C2} \right \} \] Mathematica raw input
DSolve[x^3 - y'[x] + x*(1 - x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x^2/2 - Sqrt[1 - x^2]*C[1] + C[2]}}
Maple raw input
dsolve(x*(-x^2+1)*diff(diff(y(x),x),x)-diff(y(x),x)+x^3 = 0, y(x),'implicit')
Maple raw output
y(x) = 1/2*x^2+(-1+x)^(1/2)*(1+x)^(1/2)*_C1+_C2