85.16.1 problem 1

Internal problem ID [22545]
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. B Exercises at page 48
Problem number : 1
Date solved : Thursday, October 02, 2025 at 08:49:35 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _exact, _rational]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 61

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

\begin{align*} y &= \frac {c_1}{4}+\frac {1}{4}-\frac {\sqrt {c_1^{2}+\left (8 x +2\right ) c_1 +16 \left (x -\frac {1}{4}\right )^{2}}}{4} \\ y &= \frac {c_1}{4}+\frac {1}{4}+\frac {\sqrt {c_1^{2}+\left (8 x +2\right ) c_1 +16 \left (x -\frac {1}{4}\right )^{2}}}{4} \\ \end{align*}

✓ Mathematica. Time used: 0.287 (sec). Leaf size: 76

ode=(y[x]/(x+y[x])^2 -1 )+(1- x/(x+y[x])^2 )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} \left (-\sqrt {4 x^2+4 c_1 x+(1+c_1){}^2}+1+c_1\right )\\ y(x)&\to \frac {1}{2} \left (\sqrt {4 x^2+4 c_1 x+(1+c_1){}^2}+1+c_1\right )\\ y(x)&\to -x \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-x/(x + y(x))**2 + 1)*Derivative(y(x), x) - 1 + y(x)/(x + y(x))**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out