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 : Sunday, March 30, 2025 at 12:07:30 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*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 35

ode:=x-y(x)-1+(-x+y(x)+2)*diff(y(x),x) = 0; 
dsolve(ode,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*}

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

ode=(x-y[x]-1)+(y[x]-x+2)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 1.018 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + (-x + y(x) + 2)*Derivative(y(x), x) - y(x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = x - \sqrt {C_{1} - 2 x} - 2, \ y{\left (x \right )} = x + \sqrt {C_{1} - 2 x} - 2\right ] \]