59.1.666 problem 683

Internal problem ID [9838]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 683
Date solved : Monday, January 27, 2025 at 06:14:53 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 35

dsolve(x^2*diff(y(x),x$2)+x*(6+x^2)*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{2} {\mathrm e}^{-\frac {x^{2}}{2}} \operatorname {hypergeom}\left (\left [2\right ], \left [\frac {1}{2}\right ], \frac {x^{2}}{2}\right )+c_{1} \left (x^{2}+3\right ) x}{x^{3}} \]

✓ Solution by Mathematica

Time used: 0.248 (sec). Leaf size: 50

DSolve[x^2*D[y[x],{x,2}]+x*(6+x^2)*D[y[x],x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\left (x^2+3\right ) \left (c_2 \int _1^x\frac {e^{-\frac {1}{2} K[1]^2}}{K[1]^2 \left (K[1]^2+3\right )^2}dK[1]+c_1\right )}{x^2} \]