ODE
\[ x \left (x^2+2\right ) y''(x)-y'(x)-6 x y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.205499 (sec), leaf count = 54
\[\left \{\left \{y(x)\to \frac {1}{6} \left (x^2+2\right )^{3/4} \left (6 c_1 x^{3/2}-\sqrt [4]{2} c_2 \, _2F_1\left (-\frac {3}{4},\frac {7}{4};\frac {1}{4};-\frac {x^2}{2}\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.318 (sec), leaf count = 37
\[\left [y \left (x \right ) = \textit {\_C1} \left (x^{2}+2\right )^{\frac {3}{4}} x^{\frac {3}{2}}+\textit {\_C2} \left (x^{2}+2\right )^{\frac {3}{4}} \hypergeom \left (\left [-\frac {3}{4}, \frac {7}{4}\right ], \left [\frac {1}{4}\right ], -\frac {x^{2}}{2}\right )\right ]\] Mathematica raw input
DSolve[-6*x*y[x] - y'[x] + x*(2 + x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> ((2 + x^2)^(3/4)*(6*x^(3/2)*C[1] - 2^(1/4)*C[2]*Hypergeometric2F1[-3/4, 7/4, 1/4, -1/2*x^2]))/6}}
Maple raw input
dsolve(x*(x^2+2)*diff(diff(y(x),x),x)-diff(y(x),x)-6*x*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*(x^2+2)^(3/4)*x^(3/2)+_C2*(x^2+2)^(3/4)*hypergeom([-3/4, 7/4],[1/4],-1/2*x^2)]