77.1.44 problem 61 (page 103)

Internal problem ID [17934]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 61 (page 103)
Date solved : Tuesday, January 28, 2025 at 11:13:50 AM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.149 (sec). Leaf size: 27

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

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