Internal problem ID [6825]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 93.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (1+3 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.117 (sec). Leaf size: 33
dsolve(3*x^2*diff(y(x),x$2)+x*(1+x)*diff(y(x),x)-(1+3*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x \left (x^{2}+20 x +70\right )+\frac {c_{2} {\mathrm e}^{-\frac {x}{3}} \hypergeom \left (\relax [3], \left [-\frac {1}{3}\right ], \frac {x}{3}\right )}{x^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 0.672 (sec). Leaf size: 70
DSolve[3*x^2*y''[x]+x*(1+x)*y'[x]-(1+3*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x (x (x+20)+70) \left (5040 c_1-3^{2/3} c_2 \operatorname {Gamma}\left (\frac {2}{3},\frac {x}{3}\right )\right )}{5040}+\frac {c_2 e^{-x/3} (x (x (x+19)+54)-18)}{1680 \sqrt [3]{x}} \\ \end{align*}