Internal problem ID [15022]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 5. Homogeneous equations. Exercises page 44
Problem number: 115.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y+\left (y-1+x \right ) y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
dsolve((x+y(x))+(x+y(x)-1)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y &= 1-x -\sqrt {2 c_{1} -2 x +1} \\ y &= 1-x +\sqrt {2 c_{1} -2 x +1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.123 (sec). Leaf size: 43
DSolve[(x+y[x])+(x+y[x]-1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x-\sqrt {-2 x+1+c_1}+1 \\ y(x)\to -x+\sqrt {-2 x+1+c_1}+1 \\ \end{align*}