Internal problem ID [6898]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 166.
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 +2\right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 62
dsolve(2*x^2*(2+x)*diff(y(x),x$2)-x*(4-7*x)*diff(y(x),x)-(5-3*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x^{\frac {5}{2}}}{\left (x +2\right )^{\frac {7}{2}}}+\frac {c_{2} \left (\frac {\sqrt {x +2}\, \sqrt {2}\, \left (33 x^{2}+52 x +32\right )}{33}+\frac {5 \arctanh \left (\frac {\sqrt {x +2}\, \sqrt {2}}{2}\right ) x^{3}}{11}\right )}{\sqrt {x}\, \left (x +2\right )^{\frac {7}{2}}} \]
✓ Solution by Mathematica
Time used: 0.245 (sec). Leaf size: 92
DSolve[2*x^2*(2+x)*y''[x]-x*(4-7*x)*y'[x]-(5-3*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {-48 c_1 x^3+15 \sqrt {2} c_2 x^3 \tanh ^{-1}\left (\frac {\sqrt {x+2}}{\sqrt {2}}\right )+66 c_2 \sqrt {x+2} x^2+104 c_2 \sqrt {x+2} x+64 c_2 \sqrt {x+2}}{48 \sqrt {x} (x+2)^{7/2}} \\ \end{align*}