Internal problem ID [79]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 1.
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 {\left (x +y\right ) y^{\prime }-x +y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.021 (sec). Leaf size: 51
dsolve((x+y(x))*diff(y(x),x) = x-y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-x c_{1}-\sqrt {2 c_{1}^{2} x^{2}+1}}{c_{1}} \\ y \relax (x ) = \frac {-x c_{1}+\sqrt {2 c_{1}^{2} x^{2}+1}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.164 (sec). Leaf size: 94
DSolve[(x+y[x])*y'[x]== x-y[x],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 -\sqrt {2} \sqrt {x^2}-x \\ y(x)\to \sqrt {2} \sqrt {x^2}-x \\ \end{align*}