Internal problem ID [6869]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 137.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 61
dsolve(2*x^2*(1+x)*diff(y(x),x$2)-x*(6-x)*diff(y(x),x)+(8-x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x^{2}}{\left (x +1\right )^{\frac {5}{2}}}+\frac {c_{2} x^{2} \left (2 \sqrt {x +1}\, x +8 \sqrt {x +1}+3 \ln \left (\sqrt {x +1}-1\right )-3 \ln \left (\sqrt {x +1}+1\right )\right )}{\left (x +1\right )^{\frac {5}{2}}} \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 50
DSolve[2*x^2*(1+x)*y''[x]-x*(6-x)*y'[x]+(8-x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2 \left (2 c_2 \sqrt {x+1} (x+4)-6 c_2 \tanh ^{-1}\left (\sqrt {x+1}\right )+3 c_1\right )}{3 (x+1)^{5/2}} \\ \end{align*}