59.1.441 problem 454

Internal problem ID [9613]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 454
Date solved : Monday, January 27, 2025 at 06:04:39 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 19

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

\[ y(x)\to \frac {e^x (c_2 x+c_1)}{x} \]