Internal problem ID [1927]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 7, page 28
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-y+\left (y-x +1\right ) y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 35
dsolve((x-y(x))+(y(x)-x+1)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y = x -1-\sqrt {2 c_{1} -2 x +1} y = x -1+\sqrt {2 c_{1} -2 x +1} \end{align*}
✓ Solution by Mathematica
Time used: 0.092 (sec). Leaf size: 49
DSolve[(x-y[x])+(y[x]-x+1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x-i \sqrt {2 x-1-c_1}-1 y(x)\to x+i \sqrt {2 x-1-c_1}-1 \end{align*}