Internal problem ID [3875]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 3
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _exact, _rational, _Bernoulli]
Solve \begin {gather*} \boxed {{\mathrm e}^{x} \left (x^{2}+y^{2}+2 x \right )+2 y \,{\mathrm e}^{x} y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (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 \relax (x ) = \sqrt {{\mathrm e}^{-x} c_{1}-x^{2}} \\ y \relax (x ) = -\sqrt {{\mathrm e}^{-x} c_{1}-x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 5.838 (sec). Leaf size: 47
DSolve[Exp[x]*(x^2+y[x]^2+2*x)+2*y[x]*Exp[x]*y'[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*}