Internal problem ID [6908]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 176.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.111 (sec). Leaf size: 47
dsolve(x^2*(1+2*x)*diff(y(x),x$2)+x*(9+13*x)*diff(y(x),x)+(7+5*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (143 x^{2}+104 x +20\right )}{x^{7}}+\frac {c_{2} \left (35 x^{3}-45 x^{2}+36 x -20\right ) \left (2 x +1\right )^{\frac {7}{2}}}{x^{7}} \]
✓ Solution by Mathematica
Time used: 0.848 (sec). Leaf size: 57
DSolve[x^2*(1+2*x)*y''[x]+x*(9+13*x)*y'[x]+(7+5*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 (x (5 x (7 x-9)+36)-20) (2 x+1)^{7/2}}{315 x^7}+\frac {c_1 (13 x (11 x+8)+20)}{143 x^7} \\ \end{align*}