ODE
\[ \left (x^3+1\right ) x y''(x)-\left (1-x^3\right ) y'(x)+x^2 (-y(x))=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.404493 (sec), leaf count = 44
\[\left \{\left \{y(x)\to \frac {1}{2} \sqrt [3]{x^3+1} \left (c_2 x^2 \, _2F_1\left (\frac {2}{3},\frac {4}{3};\frac {5}{3};-x^3\right )+2 c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.428 (sec), leaf count = 37
\[\left [y \left (x \right ) = \textit {\_C1} \,x^{2} \left (x^{3}+1\right )^{\frac {1}{3}} \hypergeom \left (\left [\frac {2}{3}, \frac {4}{3}\right ], \left [\frac {5}{3}\right ], -x^{3}\right )+\textit {\_C2} \left (x^{3}+1\right )^{\frac {1}{3}}\right ]\] Mathematica raw input
DSolve[-(x^2*y[x]) - (1 - x^3)*y'[x] + x*(1 + x^3)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> ((1 + x^3)^(1/3)*(2*C[1] + x^2*C[2]*Hypergeometric2F1[2/3, 4/3, 5/3, -x^3]))/2}}
Maple raw input
dsolve(x*(x^3+1)*diff(diff(y(x),x),x)-(-x^3+1)*diff(y(x),x)-x^2*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x^2*(x^3+1)^(1/3)*hypergeom([2/3, 4/3],[5/3],-x^3)+_C2*(x^3+1)^(1/3)]