85.15.4 problem 1 (d)

Internal problem ID [22529]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 47
Problem number : 1 (d)
Date solved : Thursday, October 02, 2025 at 08:46:38 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\frac {x}{x +y} \end{align*}

✓ Maple. Time used: 0.054 (sec). Leaf size: 52

ode:=diff(y(x),x) = x/(x+y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ -\frac {\ln \left (\frac {-x^{2}+x y+y^{2}}{x^{2}}\right )}{2}+\frac {\sqrt {5}\, \operatorname {arctanh}\left (\frac {\left (2 y+x \right ) \sqrt {5}}{5 x}\right )}{5}-\ln \left (x \right )-c_1 = 0 \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 63

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

\[ \text {Solve}\left [\frac {1}{10} \left (\left (5+\sqrt {5}\right ) \log \left (-\frac {2 y(x)}{x}+\sqrt {5}-1\right )-\left (\sqrt {5}-5\right ) \log \left (\frac {2 y(x)}{x}+\sqrt {5}+1\right )\right )=-\log (x)+c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out