59.1.781 problem 803

Internal problem ID [9953]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 803
Date solved : Monday, January 27, 2025 at 06:16:07 PM
CAS classification : [_Laguerre]

\begin{align*} x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 13

dsolve(x*diff(y(x),x$2)-(x+1)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} c_{2} +c_{1} x +c_{1} \]

✓ Solution by Mathematica

Time used: 0.387 (sec). Leaf size: 78

DSolve[x*D[y[x],{x,2}]-(x+1)*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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