2.38 problem 36

Internal problem ID [5033]

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]]

Solve \begin {gather*} \boxed {x -y-1+\left (2-x +y\right ) y^{\prime }=0} \end {gather*}

Solution by Maple

Time used: 0.013 (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 \relax (x ) = x -2-\sqrt {-2 x +4+2 c_{1}} \\ y \relax (x ) = x -2+\sqrt {-2 x +4+2 c_{1}} \\ \end{align*}

Solution by Mathematica

Time used: 0.09 (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*}