Internal problem ID [7682]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 101.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {x y^{\prime }+x y^{2}-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
dsolve(x*diff(y(x),x) + x*y(x)^2 - y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {2 x}{x^{2}+2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.246 (sec). Leaf size: 23
DSolve[x*y'[x] + x*y[x]^2 - y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 x}{x^2+2 c_1} \\ y(x)\to 0 \\ \end{align*}