Internal problem ID [7379]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 660.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 18
dsolve(x*diff(y(x),x$2)-(2*x+1)*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (2 x +1\right )+c_{2} {\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 25
DSolve[x*y''[x]-(2*x+1)*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{2 x}-\frac {1}{4} c_2 (2 x+1) \\ \end{align*}