32.5.18 problem Exercise 11.19, page 97

Internal problem ID [5856]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli Equations
Problem number : Exercise 11.19, page 97
Date solved : Monday, January 27, 2025 at 01:20:57 PM
CAS classification : [_Bernoulli]

\begin{align*} x y^{\prime }-y \left (2 y \ln \left (x \right )-1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(x*diff(y(x),x)-y(x)*(2*y(x)*ln(x)-1)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.150 (sec). Leaf size: 22

DSolve[x*D[y[x],x]-y[x]*(2*y[x]*Log[x]-1)==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{2 \log (x)+c_1 x+2} \\ y(x)\to 0 \\ \end{align*}