Internal problem ID [3937]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 8
Problem number: Differential equations with Linear Coefficients. Exercise 8.5, page
69.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {x +y-1-\left (x -y-1\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.03 (sec). Leaf size: 29
dsolve((x+y(x)-1)-(x-y(x)-1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\tan \left (\RootOf \left (2 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \left (x -1\right )+2 c_{1}\right )\right ) \left (x -1\right ) \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 48
DSolve[(x+y[x]-1)-(x-y[x]-1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \text {ArcTan}\left (\frac {y(x)+x-1}{-y(x)+x-1}\right )=\log \left (\frac {1}{2} \left (\frac {y(x)^2}{(x-1)^2}+1\right )\right )+2 \log (x-1)+c_1,y(x)\right ] \]