31.2.6 problem 6

Internal problem ID [5727]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 3
Problem number : 6
Date solved : Monday, January 27, 2025 at 01:11:39 PM
CAS classification : [[_homogeneous, `class D`], _exact, _rational, _Bernoulli]

\begin{align*} {\mathrm e}^{x} \left (x^{2}+y^{2}+2 x \right )+2 y \,{\mathrm e}^{x} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

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

dsolve(exp(x)*(x^2+y(x)^2+2*x)+2*y(x)*exp(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: 6.076 (sec). Leaf size: 47

DSolve[Exp[x]*(x^2+y[x]^2+2*x)+2*y[x]*Exp[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*}