Internal problem ID [7054]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 325.
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 }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.083 (sec). Leaf size: 35
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)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-x} x^{\frac {1}{3}} \hypergeom \left (\relax [2], \left [\frac {7}{3}\right ], x\right )+\frac {c_{2} {\mathrm e}^{-x} \hypergeom \left (\left [\frac {2}{3}\right ], \left [-\frac {1}{3}\right ], x\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.147 (sec). Leaf size: 43
DSolve[x^2*y''[x]+(5/3*x+x^2)*y'[x]-1/3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {(3 x-1) \left (c_2 \operatorname {Gamma}\left (\frac {1}{3},x\right )+c_1\right )}{3 x}-\frac {c_2 e^{-x}}{x^{2/3}} \\ \end{align*}