59.1.260 problem 263

Internal problem ID [9432]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 263
Date solved : Monday, January 27, 2025 at 06:02:46 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.196 (sec). Leaf size: 33

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

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