Internal problem ID [7689]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 108.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {x y^{\prime }-y^{2} \ln \relax (x )+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(x*diff(y(x),x) - y(x)^2*ln(x) + y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{1+c_{1} x +\ln \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.278 (sec). Leaf size: 20
DSolve[x*y'[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*}