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`]]
\[ \boxed {\left (y-1+x \right ) y^{\prime }-1-x +y=0} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 27
dsolve((x+y(x)-1)*diff(y(x),x)=(x-y(x)+1),y(x), singsol=all)
\[ y \left (x \right ) = 1-\frac {c_{1} x +\sqrt {2 c_{1}^{2} x^{2}+1}}{c_{1}} \]
✓ Solution by Mathematica
Time used: 0.126 (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*}