Internal problem ID [3838]
Book: Differential and integral calculus, vol II By N. Piskunov. 1974
Section: Chapter 1
Problem number: Example, page 27.
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 {y^{\prime }-\frac {x +y-3}{x -y-1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.026 (sec). Leaf size: 31
dsolve(diff(y(x),x)=(x+y(x)-3)/(x-y(x)-1),y(x), singsol=all)
\[ y \relax (x ) = 1-\tan \left (\RootOf \left (2 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \left (x -2\right )+2 c_{1}\right )\right ) \left (x -2\right ) \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 57
DSolve[y'[x]==(x+y[x]-3)/(x-y[x]-1),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \text {ArcTan}\left (\frac {y(x)+x-3}{-y(x)+x-1}\right )=\log \left (\frac {x^2+y(x)^2-2 y(x)-4 x+5}{2 (x-2)^2}\right )+2 \log (x-2)+c_1,y(x)\right ] \]