59.1.318 problem 325

Internal problem ID [9490]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 325
Date solved : Monday, January 27, 2025 at 06:03:24 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 29

dsolve(x^2*diff(y(x),x$2)+(5/3*x+x^2)*diff(y(x),x)-1/3*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} x^{{4}/{3}} \operatorname {hypergeom}\left (\left [2\right ], \left [\frac {7}{3}\right ], x\right ) {\mathrm e}^{-x}-3 c_{2} x +c_{2}}{x} \]

✓ Solution by Mathematica

Time used: 0.763 (sec). Leaf size: 52

DSolve[x^2*D[y[x],{x,2}]+(5/3*x+x^2)*D[y[x],x]-1/3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {(3 x-1) \left (c_2 \int _1^x\frac {9 e^{-K[1]} \sqrt [3]{K[1]}}{(1-3 K[1])^2}dK[1]+c_1\right )}{3 x} \]