66.1.44 problem Problem 58

Internal problem ID [13891]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 58
Date solved : Tuesday, January 28, 2025 at 06:07:38 AM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (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: 0.149 (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*}