Internal problem ID [2671]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational]
Solve \begin {gather*} \boxed {2 y \left (x +y+2\right )+\left (y^{2}-x^{2}-4 x -1\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (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 \relax (x ) = -x -2+\frac {c_{1}}{2}-\frac {\sqrt {c_{1}^{2}-4 c_{1} x -8 c_{1}+12}}{2} \\ y \relax (x ) = -x -2+\frac {c_{1}}{2}+\frac {\sqrt {c_{1}^{2}-4 c_{1} x -8 c_{1}+12}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.355 (sec). Leaf size: 74
DSolve[2*y[x]*(x+y[x]+2)+(y[x]^2-x^2-4*x-1)*y'[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*}