Internal problem ID [6869]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 138.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (4+3 x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 74
dsolve(x^2*(1+2*x)*diff(y(x),x$2)+x*(5+9*x)*diff(y(x),x)+(4+3*x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \left (2 x +1\right )^{\frac {3}{2}}}{x^{2}}+\frac {c_{2} \left (\left (x +\frac {1}{2}\right )^{2} \ln \left (\sqrt {2 x +1}-1\right )-\left (x +\frac {1}{2}\right )^{2} \ln \left (\sqrt {2 x +1}+1\right )+\sqrt {2 x +1}\, \left (x +\frac {2}{3}\right )\right )}{\sqrt {2 x +1}\, x^{2}} \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 56
DSolve[x^2*(1+2*x)*y''[x]+x*(5+9*x)*y'[x]+(4+3*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 c_2 \left (-3 (2 x+1)^{3/2} \text {arctanh}\left (\sqrt {2 x+1}\right )+6 x+4\right )+3 c_1 (2 x+1)^{3/2}}{3 x^2} \\ \end{align*}