59.1.728 problem 745

Internal problem ID [9900]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 745
Date solved : Monday, January 27, 2025 at 06:15:34 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x \left (x -1\right )^{2} y^{\prime \prime }-2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 62

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

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