63.1.58 problem 77

Internal problem ID [15498]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 77
Date solved : Thursday, October 02, 2025 at 10:18:55 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class C`], _dAlembert]

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 19

ode:=x/(x+y(x))^2+(y(x)+2*x)/(x+y(x))^2*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {x \left (\operatorname {LambertW}\left (c_1 x \right )-1\right )}{\operatorname {LambertW}\left (c_1 x \right )} \]

✓ Mathematica. Time used: 0.063 (sec). Leaf size: 33

ode=x/(x+y[x])^2+(2*x+y[x])/(x+y[x])^2*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\log \left (\frac {y(x)}{x}+1\right )-\frac {1}{\frac {y(x)}{x}+1}=-\log (x)+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x/(x + y(x))**2 + (2*x + y(x))*Derivative(y(x), x)/(x + y(x))**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

RecursionError : maximum recursion depth exceeded