47.2.38 problem 36

Internal problem ID [7454]
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
Date solved : Monday, January 27, 2025 at 03:00:33 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.012 (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 &= x -2-\sqrt {2 c_{1} -2 x +4} \\ y &= x -2+\sqrt {2 c_{1} -2 x +4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.108 (sec). Leaf size: 49

DSolve[(x-y[x]-1)+(y[x]-x+2)*D[y[x],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*}