Internal problem ID [7844]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 359.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Laguerre]
\[ \boxed {x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(x*diff(y(x),x$2)-(x+1)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (x +1\right )+{\mathrm e}^{x} c_{2} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 19
DSolve[x*y''[x]-(x+1)*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^x-c_2 (x+1) \]