Internal problem ID [7319]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 599.
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^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 33
dsolve(9*x^2*(1+x+x^2)*diff(y(x),x$2)+3*x*(1+7*x+13*x^2)*diff(y(x),x)+(1+4*x+25*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x^{\frac {1}{3}}}{x^{2}+x +1}+\frac {c_{2} x^{\frac {1}{3}} \ln \relax (x )}{x^{2}+x +1} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 27
DSolve[9*x^2*(1+x+x^2)*y''[x]+3*x*(1+7*x+13*x^2)*y'[x]+(1+4*x+25*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [3]{x} (c_2 \log (x)+c_1)}{x^2+x+1} \\ \end{align*}