Internal problem ID [6914]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 182.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 44
dsolve(x^2*(1+x)*diff(y(x),x$2)-x*(6+11*x)*diff(y(x),x)+(6+32*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (3 x^{8}+14 x^{7}+21 x^{6}\right )+c_{2} \left (35 x^{4}+42 x^{3}+21 x^{2}+4 x \right ) \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 44
DSolve[x^2*(1+x)*y''[x]-x*(6+11*x)*y'[x]+(6+32*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} c_1 x (x+1)^6 (3 x-4)-\frac {1}{140} c_2 x (7 x (x (5 x+6)+3)+4) \\ \end{align*}