Internal problem ID [6767]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 34.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 16
dsolve((2*x+1)*diff(y(x),x$2)-2*diff(y(x),x)-(2*x+3)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} c_{1}+c_{2} {\mathrm e}^{x} x \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 29
DSolve[(2*x+1)*y''[x]-2*y'[x]-(2*x+3)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x-\frac {1}{2}} \left (c_2 e^{2 x+1} x+c_1\right ) \\ \end{align*}