31.4.1 problem 1.1

Internal problem ID [5740]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 5
Problem number : 1.1
Date solved : Tuesday, March 04, 2025 at 11:34:26 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} x^{2}+y^{2}+2 x +2 y y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 37

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

\begin{align*} y \left (x \right ) &= \sqrt {{\mathrm e}^{-x} c_{1} -x^{2}} \\ y \left (x \right ) &= -\sqrt {{\mathrm e}^{-x} c_{1} -x^{2}} \\ \end{align*}

✓ Mathematica. Time used: 5.981 (sec). Leaf size: 47

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

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

✓ Sympy. Time used: 0.499 (sec). Leaf size: 29

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

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