Internal problem ID [3181]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 36.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
\[ \boxed {y^{2}+2 y^{\prime } y=-2 x -2} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve((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 {c_{1} {\mathrm e}^{-x}-2 x} y \left (x \right ) = -\sqrt {c_{1} {\mathrm e}^{-x}-2 x} \end{align*}
✓ Solution by Mathematica
Time used: 3.531 (sec). Leaf size: 43
DSolve[(2+y[x]^2+2*x)+(2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-2 x+c_1 e^{-x}} y(x)\to \sqrt {-2 x+c_1 e^{-x}} \end{align*}