59.1.230 problem 233

Internal problem ID [9402]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 233
Date solved : Monday, January 27, 2025 at 06:02:22 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 x^{2} y^{\prime \prime }-x \left (x +8\right ) y^{\prime }+6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.052 (sec). Leaf size: 38

dsolve(3*x^2*diff(y(x),x$2)-x*(x+8)*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
 

\[ y = c_{2} \left (x^{{2}/{3}}-\frac {x^{{5}/{3}}}{2}+\frac {x^{{8}/{3}}}{4}\right ) {\mathrm e}^{\frac {x}{3}}+c_{1} \operatorname {hypergeom}\left (\left [3\right ], \left [\frac {10}{3}\right ], \frac {x}{3}\right ) x^{3} \]

✓ Solution by Mathematica

Time used: 0.818 (sec). Leaf size: 99

DSolve[3*x^2*D[y[x],{x,2}]-x*(x+8)*D[y[x],x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^{4/3} \left (x^2-2 x+4\right ) \exp \left (\frac {1}{6} \left (6 \int _1^x\frac {K[1]-4}{6 K[1]}dK[1]+x+8\right )\right ) \left (c_2 \int _1^x\frac {\exp \left (-2 \int _1^{K[2]}\frac {K[1]-4}{6 K[1]}dK[1]\right )}{\left (K[2]^2-2 K[2]+4\right )^2}dK[2]+c_1\right ) \]