60.3.261 problem 1266

Internal problem ID [11271]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1266
Date solved : Monday, January 27, 2025 at 11:04:45 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: 0.003 (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)
 

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

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 22

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

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