Internal problem ID [7831]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 346.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(x*diff(y(x),x$2)+(2*x+1)*diff(y(x),x)+(x+1)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x} c_{1} +c_{2} {\mathrm e}^{-x} \ln \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 19
DSolve[x*y''[x]+(2*x+1)*y'[x]+(x+1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} (c_2 \log (x)+c_1) \]