78.3.15 problem 5 (c)

Internal problem ID [18047]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 7 (Homogeneous Equations). Problems at page 67
Problem number : 5 (c)
Date solved : Monday, March 31, 2025 at 04:59:54 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 31

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

\[ y = -\tan \left (\operatorname {RootOf}\left (-2 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x -1\right )+2 c_1 \right )\right ) \left (x -1\right )+x \]

✓ Mathematica. Time used: 0.054 (sec). Leaf size: 60

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

\[ \text {Solve}\left [2 \arctan \left (\frac {y(x)-2 x+1}{y(x)-1}\right )+\log \left (\frac {2 x^2-2 x y(x)+y(x)^2-2 x+1}{2 (x-1)^2}\right )+2 \log (x-1)+c_1=0,y(x)\right ] \]

✓ Sympy. Time used: 3.678 (sec). Leaf size: 46

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

\[ \log {\left (x - 1 \right )} = C_{1} - \log {\left (\sqrt {2 - \frac {2 \left (y{\left (x \right )} - 1\right )}{x - 1} + \frac {\left (y{\left (x \right )} - 1\right )^{2}}{\left (x - 1\right )^{2}}} \right )} + \operatorname {atan}{\left (1 - \frac {y{\left (x \right )} - 1}{x - 1} \right )} \]