28.1.35 problem 35

Internal problem ID [4341]
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 : 35
Date solved : Monday, January 27, 2025 at 09:06:10 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational]

\begin{align*} 2 y \left (x +y+2\right )+\left (y^{2}-x^{2}-4 x -1\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 55

dsolve(2*y(x)*(x+y(x)+2)+(y(x)^2-x^2-4*x-1)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -x -2+\frac {c_{1}}{2}-\frac {\sqrt {12+c_{1}^{2}+\left (-4 x -8\right ) c_{1}}}{2} \\ y \left (x \right ) &= -x -2+\frac {c_{1}}{2}+\frac {\sqrt {12+c_{1}^{2}+\left (-4 x -8\right ) c_{1}}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.415 (sec). Leaf size: 74

DSolve[2*y[x]*(x+y[x]+2)+(y[x]^2-x^2-4*x-1)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{2} \left (-2 x-\sqrt {4 (-4+c_1) x-4+c_1{}^2}-c_1\right ) \\ y(x)\to \frac {1}{2} \left (-2 x+\sqrt {4 (-4+c_1) x-4+c_1{}^2}-c_1\right ) \\ y(x)\to 0 \\ \end{align*}