Internal problem ID [5030]
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.
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 +3 y-5}{x -y-1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.485 (sec). Leaf size: 29
dsolve(diff(y(x),x)=(x+3*y(x)-5)/(x-y(x)-1),y(x), singsol=all)
\[ y \relax (x ) = 1-\frac {\left (x -2\right ) \left (\LambertW \left (2 c_{1} \left (x -2\right )\right )+2\right )}{\LambertW \left (2 c_{1} \left (x -2\right )\right )} \]
✓ Solution by Mathematica
Time used: 1.754 (sec). Leaf size: 148
DSolve[y'[x]==(x+3*y[x]-5)/(x-y[x]-1),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {2^{2/3} \left (x \log \left (-\frac {y(x)+x-3}{-y(x)+x-1}\right )-(x-3) \log \left (\frac {x-2}{-y(x)+x-1}\right )-3 \log \left (-\frac {y(x)+x-3}{-y(x)+x-1}\right )-y(x) \left (\log \left (\frac {x-2}{-y(x)+x-1}\right )-\log \left (-\frac {y(x)+x-3}{-y(x)+x-1}\right )+1+\log (2)\right )+x-x \log (6)+x \log (3)-1+\log (8)\right )}{9 (y(x)+x-3)}=\frac {1}{9} 2^{2/3} \log (x-2)+c_1,y(x)\right ] \]