Internal problem ID [8846]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1266.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (x -2\right )^{2} y^{\prime \prime }-\left (x -2\right ) y^{\prime }-3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 19
dsolve((x-2)^2*diff(diff(y(x),x),x)-(x-2)*diff(y(x),x)-3*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x -2}+c_{2} \left (x -2\right )^{3} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 22
DSolve[-3*y[x] - (-2 + x)*y'[x] + (-2 + x)^2*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*}