Internal problem ID [7980]
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]]
\[ \boxed {\left (3 x +1\right ) y^{\prime \prime }+x y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 56
dsolve((1+3*x)*diff(y(x),x$2)+x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (3 x +1\right )^{\frac {10}{9}} {\mathrm e}^{-\frac {x}{3}} \left (x -6\right )+c_{2} \left (3 x +1\right )^{\frac {10}{9}} {\mathrm e}^{-\frac {x}{3}} \left (x -6\right ) \left (\int \frac {{\mathrm e}^{\frac {x}{3}}}{\left (x -6\right )^{2} \left (3 x +1\right )^{\frac {19}{9}}}d x \right ) \]
✓ Solution by Mathematica
Time used: 0.9 (sec). Leaf size: 124
DSolve[(1+3*x)*y''[x]+x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-\frac {x}{3}-\frac {1}{9}} \left (1520 c_1 \sqrt [9]{3 x+1} \left (3 x^2-17 x-6\right )-2^{8/9} c_2 e^{\frac {x}{3}+\frac {1}{9}} \left (9 x^2-48 x-26\right )+2^{8/9} 3^{7/9} c_2 \sqrt [9]{-3 x-1} \left (3 x^2-17 x-6\right ) \Gamma \left (\frac {8}{9},\frac {1}{9} (-3 x-1)\right )\right )}{380\ 2^{17/18}} \]