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 = 0.186632 (sec), leaf count = 30
\[\left \{\left \{y(x)\to \frac {x^2}{2}-c_1 \sqrt {1-x^2}+c_2\right \}\right \}\]
Maple ✓
cpu = 0.165 (sec), leaf count = 23
\[\left [y \left (x \right ) = \frac {x^{2}}{2}+\sqrt {x -1}\, \sqrt {x +1}\, \textit {\_C1} +\textit {\_C2}\right ]\] 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))
Maple raw output
[y(x) = 1/2*x^2+(x-1)^(1/2)*(x+1)^(1/2)*_C1+_C2]