60.3.322 problem 1328

Internal problem ID [11332]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1328
Date solved : Monday, January 27, 2025 at 11:15:18 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 0.060 (sec). Leaf size: 62

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

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