47.2.35 problem 33

Internal problem ID [7451]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems. page 12
Problem number : 33
Date solved : Monday, January 27, 2025 at 03:00:26 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {x +3 y-5}{x -y-1} \end{align*}

✓ Solution by Maple

Time used: 0.109 (sec). Leaf size: 32

dsolve(diff(y(x),x)=(x+3*y(x)-5)/(x-y(x)-1),y(x), singsol=all)
 

\[ y = \frac {\left (3-x \right ) \operatorname {LambertW}\left (2 c_{1} \left (x -2\right )\right )-2 x +4}{\operatorname {LambertW}\left (2 c_{1} \left (x -2\right )\right )} \]

✓ Solution by Mathematica

Time used: 0.964 (sec). Leaf size: 148

DSolve[D[y[x],x]==(x+3*y[x]-5)/(x-y[x]-1),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [-\frac {2^{2/3} \left (x \log \left (-\frac {y(x)+x-3}{-y(x)+x-1}\right )-(x-3) \log \left (\frac {x-2}{-y(x)+x-1}\right )-3 \log \left (-\frac {y(x)+x-3}{-y(x)+x-1}\right )-y(x) \left (\log \left (\frac {x-2}{-y(x)+x-1}\right )-\log \left (-\frac {y(x)+x-3}{-y(x)+x-1}\right )+1+\log (2)\right )+x-x \log (6)+x \log (3)-1+\log (8)\right )}{9 (y(x)+x-3)}=\frac {1}{9} 2^{2/3} \log (x-2)+c_1,y(x)\right ] \]