60.1.109 problem 109

Internal problem ID [10123]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 109
Date solved : Monday, January 27, 2025 at 06:28:29 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: 0.004 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.149 (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*}