Internal problem ID [7402]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 683.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 36
dsolve(x^2*diff(y(x),x$2)+x*(6+x^2)*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (x^{2}+3\right )}{x^{2}}+\frac {c_{2} {\mathrm e}^{-\frac {x^{2}}{2}} \hypergeom \left (\relax [2], \left [\frac {1}{2}\right ], \frac {x^{2}}{2}\right )}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.122 (sec). Leaf size: 63
DSolve[x^2*y''[x]+x*(6+x^2)*y'[x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2 c_2 e^{-\frac {x^2}{2}} \left (x^2+2\right )-x \left (x^2+3\right ) \left (12 c_1-\sqrt {2 \pi } c_2 \text {Erf}\left (\frac {x}{\sqrt {2}}\right )\right )}{12 x^3} \\ \end{align*}