Internal problem ID [2594]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, section 10, page 47
Problem number: 4(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational]
Solve \begin {gather*} \boxed {\left (x -1-y^{2}\right ) y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve((x-1-y(x)^2)*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {c_{1}}{2}-\frac {\sqrt {c_{1}^{2}-4 x +4}}{2} \\ y \relax (x ) = \frac {c_{1}}{2}+\frac {\sqrt {c_{1}^{2}-4 x +4}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.324 (sec). Leaf size: 56
DSolve[(x-1-y[x]^2)*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (c_1-\sqrt {-4 x+4+c_1{}^2}\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {-4 x+4+c_1{}^2}+c_1\right ) \\ y(x)\to 0 \\ \end{align*}