59.3.12 problem Carolyn J. Smith 1984 paper. Appendix B examples and tests. Example 3

Internal problem ID [10014]
Book : Collection of Kovacic problems
Section : section 3. Problems from Kovacic related papers
Problem number : Carolyn J. Smith 1984 paper. Appendix B examples and tests. Example 3
Date solved : Monday, January 27, 2025 at 06:18:16 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (x -2\right )^{2} y^{\prime \prime }-\left (x -2\right ) y^{\prime }-3 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 19

dsolve((x-2)^2*diff(y(x),x$2)-(x-2)*diff(y(x),x)-3*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {\left (x -2\right )^{4} c_{1} +c_{2}}{x -2} \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 22

DSolve[(x-2)^2*D[y[x],{x,2}]-(x-2)*D[y[x],x]-3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 (x-2)^3+\frac {c_2}{x-2} \]