Internal problem ID [8691]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1111.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Laguerre]
Solve \begin {gather*} \boxed {y^{\prime \prime } x -\left (x +1\right ) y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 14
dsolve(x*diff(diff(y(x),x),x)-(x+1)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (x +1\right )+c_{2} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 19
DSolve[y[x] - (1 + x)*y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^x-c_2 (x+1) \\ \end{align*}