32.10.22 problem Exercise 35.23(a), page 504

Internal problem ID [6016]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 8. Special second order equations. Lesson 35. Independent variable x absent
Problem number : Exercise 35.23(a), page 504
Date solved : Monday, January 27, 2025 at 01:32:36 PM
CAS classification : [_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+y^{\prime } y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 18

dsolve(x*y(x)*diff(y(x),x$2)-2*x*(diff(y(x),x))^2+y(x)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y &= -\frac {1}{c_1 \ln \left (x \right )+c_2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.252 (sec). Leaf size: 22

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

\begin{align*} y(x)\to \frac {c_2}{-\log (x)+c_1} \\ y(x)\to 0 \\ \end{align*}