Internal problem ID [8896]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1319.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {x \left (x^{2}+2\right ) y^{\prime \prime }-y^{\prime }-6 y x=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 37
dsolve(x*(x^2+2)*diff(diff(y(x),x),x)-diff(y(x),x)-6*x*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x^{\frac {3}{2}} \left (x^{2}+2\right )^{\frac {3}{4}}+c_{2} \left (x^{2}+2\right )^{\frac {3}{4}} \operatorname {hypergeom}\left (\left [-\frac {3}{4}, \frac {7}{4}\right ], \left [\frac {1}{4}\right ], -\frac {x^{2}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 10.04 (sec). Leaf size: 54
DSolve[-6*x*y[x] - y'[x] + x*(2 + x^2)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 \operatorname {Hypergeometric2F1}\left (-\frac {3}{4},\frac {7}{4},\frac {1}{4},-\frac {x^2}{2}\right )\right ) \\ \end{align*}