Internal problem ID [1989]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number: Problem 14.15.
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 +3 y-4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.024 (sec). Leaf size: 29
dsolve(diff(y(x),x) = - (x+y(x))/(3*x+3*y(x)-4),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\LambertW \left (\frac {3 \,{\mathrm e}^{-3} {\mathrm e}^{x} {\mathrm e}^{-c_{1}}}{2}\right )-3+x -c_{1}}+2-x \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 24
DSolve[y'[x] == - (x+y[x])/(3*x+3*y[x]-4),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2}{3} \text {ProductLog}\left (-e^{x-1+c_1}\right )-x+2 \\ \end{align*}