Internal problem ID [6903]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 171.
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 (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.188 (sec). Leaf size: 57
dsolve(2*x^2*(2+3*x)*diff(y(x),x$2)+x*(4+21*x)*diff(y(x),x)-(1-9*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sqrt {x}}{\left (3 x +2\right )^{\frac {3}{2}}}+\frac {c_{2} \left (\sqrt {3 x +2}\, \sqrt {2}+3 \arctanh \left (\frac {\sqrt {3 x +2}\, \sqrt {2}}{2}\right ) x \right )}{\sqrt {x}\, \left (3 x +2\right )^{\frac {3}{2}}} \]
✓ Solution by Mathematica
Time used: 0.132 (sec). Leaf size: 64
DSolve[2*x^2*(2+3*x)*y''[x]+x*(4+21*x)*y'[x]-(1-9*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {-2 c_1 x+2 c_2 \sqrt {3 x+2}+3 \sqrt {2} c_2 x \tanh ^{-1}\left (\sqrt {\frac {3 x}{2}+1}\right )}{2 \sqrt {x} (3 x+2)^{3/2}} \\ \end{align*}