59.1.261 problem 264

Internal problem ID [9433]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 264
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: 0.004 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.207 (sec). Leaf size: 36

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

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