8.5.18 problem 18

Internal problem ID [746]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 18
Date solved : Tuesday, March 04, 2025 at 11:40:25 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 11

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

\begin{align*} y &= -x \\ y &= c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 14

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

\begin{align*} y(x)\to -x \\ y(x)\to c_1 \\ \end{align*}

✓ Sympy. Time used: 0.170 (sec). Leaf size: 8

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

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