Internal problem ID [7887]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 407.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (1+x \right ) y^{\prime \prime }-\left (x +2\right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve((x+1)*diff(y(x),x$2)-(x+2)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (x +2\right )+{\mathrm e}^{x} c_{2} \]
✓ Solution by Mathematica
Time used: 0.15 (sec). Leaf size: 29
DSolve[(x+1)*y''[x]-(x+2)*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1 e^{x+1}-2 c_2 (x+2)}{\sqrt {2 e}} \]