28.1.36 problem 36

Internal problem ID [4342]
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
Date solved : Monday, January 27, 2025 at 09:06:14 AM
CAS classification : [_rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.012 (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 {{\mathrm e}^{-x} c_{1} -2 x} \\ y \left (x \right ) &= -\sqrt {{\mathrm e}^{-x} c_{1} -2 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 3.623 (sec). Leaf size: 43

DSolve[(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 {-2 x+c_1 e^{-x}} \\ y(x)\to \sqrt {-2 x+c_1 e^{-x}} \\ \end{align*}