82.8.1 problem Ex. 1

Internal problem ID [18749]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Exercises at page 25
Problem number : Ex. 1
Date solved : Tuesday, January 28, 2025 at 12:14:22 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: 0.006 (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: 5.839 (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*}