Internal problem ID [7581]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (-2+x \right )^{2} y^{\prime \prime }-\left (-2+x \right ) y^{\prime }-3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \relax (x ) = c_{1} \left (x -2\right )^{3}+\frac {c_{2}}{x -2} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 22
DSolve[(x-2)^2*y''[x]-(x-2)*y'[x]-3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 (x-2)^3+\frac {c_2}{x-2} \\ \end{align*}