60.1.108 problem 108

Internal problem ID [10122]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 108
Date solved : Monday, January 27, 2025 at 06:28:27 PM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.154 (sec). Leaf size: 20

DSolve[x*D[y[x],x] - y[x]^2*Log[x] + y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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