Internal problem ID [2498]
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`]]
\[ \boxed {y^{\prime }+\frac {y+x}{3 x +3 y-4}=0} \]
✓ Solution by Maple
Time used: 0.031 (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: 3.788 (sec). Leaf size: 33
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} W\left (-e^{x-1+c_1}\right )-x+2 \\ y(x)\to 2-x \\ \end{align*}