Internal problem ID [7286]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 566.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 15.063 (sec). Leaf size: 38
dsolve(9*x^2*(1+x)*diff(y(x),x$2)+3*x*(5+11*x-x^2)*diff(y(x),x)+(1+16*x-7*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \HeunC \left (-\frac {1}{3}, -\frac {4}{3}, 0, -\frac {1}{9}, \frac {11}{18}, x +1\right )}{\left (x +1\right )^{\frac {4}{3}} x^{\frac {1}{3}}}+\frac {c_{2} \HeunC \left (-\frac {1}{3}, \frac {4}{3}, 0, -\frac {1}{9}, \frac {11}{18}, x +1\right )}{x^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 1.973 (sec). Leaf size: 59
DSolve[9*x^2*(1+x)*y''[x]+3*x*(5+11*x-x^2)*y'[x]+(1+16*x-7*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{x/3} \left (c_2 \int _1^x\frac {e^{-\frac {K[1]}{3}} \sqrt [3]{K[1]+1}}{K[1]}dK[1]+c_1\right )}{\sqrt [3]{x} (x+1)^{4/3}} \\ \end{align*}