Internal problem ID [2569]
Book: Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section: Chapter 11.3, page 316
Problem number: 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _exact, _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\left (x +y-1\right ) y^{\prime }-1-x +y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.25 (sec). Leaf size: 27
dsolve((x+y(x)-1)*diff(y(x),x)=(x-y(x)+1),y(x), singsol=all)
\[ y \relax (x ) = 1-\frac {x c_{1}+\sqrt {2 x^{2} c_{1}^{2}+1}}{c_{1}} \]
✓ Solution by Mathematica
Time used: 0.172 (sec). Leaf size: 47
DSolve[(x+y[x]-1)*y'[x]==(x-y[x]+1),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {2 x^2+1+c_1}-x+1 \\ y(x)\to \sqrt {2 x^2+1+c_1}-x+1 \\ \end{align*}