Internal problem ID [1928]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 7, page 28
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {x +y-1}{-y+x -1}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve(diff(y(x),x)=(x+y(x)-1)/(x-y(x)-1),y(x), singsol=all)
\[ y = -\tan \left (\operatorname {RootOf}\left (2 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \left (x -1\right )+2 c_{1} \right )\right ) \left (x -1\right ) \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 48
DSolve[y'[x]==(x+y[x]-1)/(x-y[x]-1),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \arctan \left (\frac {y(x)+x-1}{-y(x)+x-1}\right )=\log \left (\frac {1}{2} \left (\frac {y(x)^2}{(x-1)^2}+1\right )\right )+2 \log (x-1)+c_1,y(x)\right ] \]