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 : Monday, January 27, 2025 at 01:12:22 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Solution by Maple

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

dsolve((x^2+y(x)^2+2*x)+2*y(x)*diff(y(x),x)=0,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*}

✓ Solution by Mathematica

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

DSolve[(x^2+y[x]^2+2*x)+2*y[x]*D[y[x],x]==0,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*}