59.2.8 problem 8

Internal problem ID [10001]
Book : Collection of Kovacic problems
Section : section 2. Solution found using all possible Kovacic cases
Problem number : 8
Date solved : Monday, January 27, 2025 at 06:16:37 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.391 (sec). Leaf size: 75

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

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