30.1.2 problem Example, page 27

Internal problem ID [5690]
Book : Differential and integral calculus, vol II By N. Piskunov. 1974
Section : Chapter 1
Problem number : Example, page 27
Date solved : Monday, January 27, 2025 at 01:07:16 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {x +y-3}{x -y-1} \end{align*}

✓ Solution by Maple

Time used: 0.051 (sec). Leaf size: 32

dsolve(diff(y(x),x)=(x+y(x)-3)/(x-y(x)-1),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.063 (sec). Leaf size: 57

DSolve[D[y[x],x]==(x+y[x]-3)/(x-y[x]-1),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [2 \arctan \left (\frac {y(x)+x-3}{-y(x)+x-1}\right )=\log \left (\frac {x^2+y(x)^2-2 y(x)-4 x+5}{2 (x-2)^2}\right )+2 \log (x-2)+c_1,y(x)\right ] \]