Internal problem ID [6215]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-2 y+\left (-1+y\right ) y^{\prime }=-2 x} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 31
dsolve((2*x-2*y(x))+(y(x)-1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\tan \left (\operatorname {RootOf}\left (-2 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \left (x -1\right )+2 c_{1} \right )\right ) \left (x -1\right )+x \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 60
DSolve[(2*x-2*y[x])+(y[x]-1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \arctan \left (\frac {y(x)-2 x+1}{y(x)-1}\right )+\log \left (\frac {2 x^2-2 x y(x)+y(x)^2-2 x+1}{2 (x-1)^2}\right )+2 \log (x-1)+c_1=0,y(x)\right ] \]