81.15.5 problem 19-5

Internal problem ID [21713]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 19. Change of variables. Page 483
Problem number : 19-5
Date solved : Thursday, October 02, 2025 at 08:00:40 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x +y-3+\left (x +y-1\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.155 (sec). Leaf size: 30

ode:=2*x+y(x)-3+(x+y(x)-1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-c_1 x +c_1 -\sqrt {-\left (x -2\right )^{2} c_1^{2}+1}}{c_1} \]

✓ Mathematica. Time used: 0.088 (sec). Leaf size: 53

ode=(2*x+y[x]-3)+(x+y[x]-1)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {-x^2+4 x+1+c_1}-x+1\\ y(x)&\to \sqrt {-x^2+4 x+1+c_1}-x+1 \end{align*}

✓ Sympy. Time used: 1.194 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x + (x + y(x) - 1)*Derivative(y(x), x) + y(x) - 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - x - \sqrt {C_{1} - x^{2} + 4 x} + 1, \ y{\left (x \right )} = - x + \sqrt {C_{1} - x^{2} + 4 x} + 1\right ] \]