Internal problem ID [7335]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 615.
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 }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 57
dsolve(x^2*(1+2*x)*diff(y(x),x$2)-2*x*(3+14*x)*diff(y(x),x)+(6+100*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (2016 x^{5}+672 x^{4}+144 x^{3}+18 x^{2}+x \right )+c_{2} \left (8 x^{10}+36 x^{9}+72 x^{8}+84 x^{7}+63 x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 44
DSolve[x^2*(1+2*x)*y''[x]-2*x*(3+14*x)*y'[x]+(6+100*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x (2 x+1)^9-\frac {c_2 x (6 x (8 x (14 x (3 x+1)+3)+3)+1)}{20160} \\ \end{align*}