60.3.407 problem 1413

Internal problem ID [11417]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1413
Date solved : Monday, January 27, 2025 at 11:20:20 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Solution by Maple

Time used: 0.153 (sec). Leaf size: 12

dsolve(diff(diff(y(x),x),x) = 1/x/(ln(x)-1)*diff(y(x),x)-1/x^2/(ln(x)-1)*y(x),y(x), singsol=all)
 
\[ y = c_{1} x +c_{2} \ln \left (x \right ) \]

Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 16

DSolve[D[y[x],{x,2}] == -(y[x]/(x^2*(-1 + Log[x]))) + D[y[x],x]/(x*(-1 + Log[x])),y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to c_1 x-c_2 \log (x) \]