8.5.1 problem 1

Internal problem ID [729]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 1
Date solved : Saturday, March 29, 2025 at 10:16:15 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 51

ode:=(x+y(x))*diff(y(x),x) = x-y(x); 
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: 0.414 (sec). Leaf size: 94

ode=(x+y[x])*D[y[x],x]== x-y[x]; 
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: 1.101 (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)
 

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