Internal problem ID [11812]
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 29.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]
\[ \boxed {y^{\prime }-\frac {y}{x +1}+y^{2}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve(diff(y(x),x)-y(x)/(1+x)+y(x)^2=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {2+2 x}{x^{2}+2 c_{1} +2 x} \]
✓ Solution by Mathematica
Time used: 0.297 (sec). Leaf size: 28
DSolve[y'[x]-y[x]/(1+x)+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 (x+1)}{x^2+2 x+2 c_1} y(x)\to 0 \end{align*}