Internal problem ID [5786]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations
problems. page 12
Problem number: 36.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-y+\left (y-x +2\right ) y^{\prime }=1-x} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 35
dsolve((x-y(x)-1)+(y(x)-x+2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= x -2-\sqrt {2 c_{1} -2 x +4} \\ y \left (x \right ) &= x -2+\sqrt {2 c_{1} -2 x +4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.102 (sec). Leaf size: 49
DSolve[(x-y[x]-1)+(y[x]-x+2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x-i \sqrt {2 x-4-c_1}-2 \\ y(x)\to x+i \sqrt {2 x-4-c_1}-2 \\ \end{align*}