Internal problem ID [15018]
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: 111.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y+\left (x -y-2\right ) y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 30
dsolve((x+y(x))+(x-y(x)-2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y = \frac {-\sqrt {2 \left (-1+x \right )^{2} c_{1}^{2}+1}+\left (x -2\right ) c_{1}}{c_{1}} \]
✓ Solution by Mathematica
Time used: 0.117 (sec). Leaf size: 59
DSolve[(x+y[x])+(x-y[x]-2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -i \sqrt {-2 x^2+4 x-4-c_1}+x-2 \\ y(x)\to i \sqrt {-2 x^2+4 x-4-c_1}+x-2 \\ \end{align*}