Internal problem ID [7239]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 519.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.797 (sec). Leaf size: 38
dsolve(3*x^2*diff(y(x),x$2)+2*x*(1+x-2*x^2)*diff(y(x),x)+(2*x-8*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{\frac {1}{3}} {\mathrm e}^{\frac {2 \left (x -1\right ) x}{3}}+c_{2} \mathit {HB}\left (-\frac {1}{3}, \frac {\sqrt {6}}{3}, -\frac {7}{3}, \frac {4 \sqrt {6}}{9}, -\frac {\sqrt {6}\, x}{3}\right ) \]
✓ Solution by Mathematica
Time used: 1.809 (sec). Leaf size: 53
DSolve[3*x^2*y''[x]+2*x*(1+x-2*x^2)*y'[x]+(2*x-8*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{\frac {2}{3} (x-1) x} \sqrt [3]{x} \left (c_2 \int _1^x\frac {e^{-\frac {2}{3} (K[1]-1) K[1]}}{K[1]^{4/3}}dK[1]+c_1\right ) \\ \end{align*}