18.1.13 problem Problem 14.15

Internal problem ID [3469]
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
Date solved : Monday, January 27, 2025 at 07:38:05 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=-\frac {x +y}{3 x +3 y-4} \end{align*}

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 21

dsolve(diff(y(x),x) = - (x+y(x))/(3*x+3*y(x)-4),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 3.144 (sec). Leaf size: 33

DSolve[D[y[x],x] == - (x+y[x])/(3*x+3*y[x]-4),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {2}{3} W\left (-e^{x-1+c_1}\right )-x+2 \\ y(x)\to 2-x \\ \end{align*}