59.1.762 problem 784

Internal problem ID [9934]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 784
Date solved : Monday, January 27, 2025 at 06:15:56 PM
CAS classification : [_Laguerre]

\begin{align*} x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

dsolve(x*diff(y(x),x$2)-(x+2)*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} c_{1} +c_{2} \left (x^{2}+2 x +2\right ) \]

✓ Solution by Mathematica

Time used: 0.222 (sec). Leaf size: 35

DSolve[x*D[y[x],{x,2}]-(x+2)*D[y[x],x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{x+1} \left (c_2 \int _1^xe^{-K[1]} K[1]^2dK[1]+c_1\right ) \]