Internal problem ID [1910]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 6, page 25
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _exact, _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {x +y+\left (x -y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 49
dsolve((x+y(x))+(x-y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {x c_{1}-\sqrt {2 x^{2} c_{1}^{2}+1}}{c_{1}} \\ y \relax (x ) = \frac {x c_{1}+\sqrt {2 x^{2} c_{1}^{2}+1}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.512 (sec). Leaf size: 86
DSolve[(x+y[x])+(x-y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x-\sqrt {2 x^2+e^{2 c_1}} \\ y(x)\to x+\sqrt {2 x^2+e^{2 c_1}} \\ y(x)\to x-\sqrt {2} \sqrt {x^2} \\ y(x)\to \sqrt {2} \sqrt {x^2}+x \\ \end{align*}