Internal problem ID [7223]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 504.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (1+3 x \right ) y^{\prime \prime }+y^{\prime } x +2 y=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 42
dsolve((1+3*x)*diff(y(x),x$2)+x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-\frac {x}{3}} \operatorname {KummerM}\left (-\frac {19}{9}, -\frac {1}{9}, \frac {x}{3}+\frac {1}{9}\right )+c_{2} \left (3 x^{2}-17 x -6\right ) {\mathrm e}^{-\frac {x}{3}} \left (\frac {x}{3}+\frac {1}{9}\right )^{\frac {1}{9}} \]
✓ Solution by Mathematica
Time used: 0.394 (sec). Leaf size: 106
DSolve[(1+3*x)*y''[x]+x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-\frac {x}{3}-\frac {1}{9}} \left (-\frac {1}{3} 2^{8/9} c_2 (x-6) (3 x+1)^2 \operatorname {ExpIntegralE}\left (\frac {1}{9},\frac {1}{9} (-3 x-1)\right )-2^{8/9} c_2 e^{\frac {x}{3}+\frac {1}{9}} \left (9 x^2-48 x-26\right )+1520 c_1 (x-6) (3 x+1)^{10/9}\right )}{380\ 2^{17/18}} \\ \end{align*}