50.5.13 problem 4(c)

Internal problem ID [7883]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.7. Homogeneous Equations. Page 28
Problem number : 4(c)
Date solved : Monday, January 27, 2025 at 03:30:44 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*}

✓ Solution by Maple

Time used: 0.041 (sec). Leaf size: 31

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

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

✓ Solution by Mathematica

Time used: 0.052 (sec). Leaf size: 60

DSolve[(2*x-2*y[x])+(y[x]-1)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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