60.3.317 problem 1323

Internal problem ID [11327]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1323
Date solved : Monday, January 27, 2025 at 11:13:20 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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

\[ y = \frac {c_{1} +c_{2} \left (x -1\right )^{3}}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.318 (sec). Leaf size: 60

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

\[ y(x)\to \frac {\left (-c_2 x \left (x^2-3 x+3\right )-3 c_1\right ) \exp \left (-\frac {1}{2} \int _1^x\left (\frac {4}{K[1]}-\frac {2}{K[1]-1}\right )dK[1]\right )}{3 (x-1)} \]