44.5.6 problem 1(f)

Internal problem ID [9162]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.7. Homogeneous Equations. Page 28
Problem number : 1(f)
Date solved : Tuesday, September 30, 2025 at 06:10:53 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.013 (sec). Leaf size: 51

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

\begin{align*} y &= \frac {-c_1 x -\sqrt {2 x^{2} c_1^{2}+1}}{c_1} \\ y &= \frac {-c_1 x +\sqrt {2 x^{2} c_1^{2}+1}}{c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.258 (sec). Leaf size: 94

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

\begin{align*} y(x)&\to -x-\sqrt {2 x^2+e^{2 c_1}}\\ y(x)&\to -x+\sqrt {2 x^2+e^{2 c_1}}\\ y(x)&\to -\sqrt {2} \sqrt {x^2}-x\\ y(x)&\to \sqrt {2} \sqrt {x^2}-x \end{align*}

✓ Sympy. Time used: 0.684 (sec). Leaf size: 29

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

\[ \left [ y{\left (x \right )} = - x - \sqrt {C_{1} + 2 x^{2}}, \ y{\left (x \right )} = - x + \sqrt {C_{1} + 2 x^{2}}\right ] \]