66.1.21 problem Problem 29

Internal problem ID [13868]
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
Date solved : Tuesday, January 28, 2025 at 06:06:15 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

\begin{align*} y^{\prime }-\frac {y}{1+x}+y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve(diff(y(x),x)-y(x)/(1+x)+y(x)^2=0,y(x), singsol=all)
 

\[ y = \frac {2+2 x}{x^{2}+2 c_{1} +2 x} \]

✓ Solution by Mathematica

Time used: 0.202 (sec). Leaf size: 28

DSolve[D[y[x],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*}