Internal problem ID [8047]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 571.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (-x +6\right ) y^{\prime }+\left (8-x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 59
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)
\[ y \left (x \right ) = \frac {c_{1} x^{2}}{\left (x +1\right )^{\frac {5}{2}}}+\frac {c_{2} x^{2} \left (\frac {2 \sqrt {x +1}\, x}{3}+\frac {8 \sqrt {x +1}}{3}+\ln \left (\sqrt {x +1}-1\right )-\ln \left (\sqrt {x +1}+1\right )\right )}{\left (x +1\right )^{\frac {5}{2}}} \]
✓ Solution by Mathematica
Time used: 0.072 (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]
\[ y(x)\to \frac {x^2 \left (-6 c_2 \text {arctanh}\left (\sqrt {x+1}\right )+2 c_2 \sqrt {x+1} (x+4)+3 c_1\right )}{3 (x+1)^{5/2}} \]