Internal problem ID [5102]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 24. First order differential equations. Further problems 24. page
1068
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (3 x +3 y-4\right ) y^{\prime }+y=-x} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 21
dsolve((3*x+3*y(x)-4)*diff(y(x),x)=-(x+y(x)),y(x), singsol=all)
\[ y \left (x \right ) = \frac {2 \operatorname {LambertW}\left (\frac {3 \,{\mathrm e}^{-3+x -c_{1}}}{2}\right )}{3}-x +2 \]
✓ Solution by Mathematica
Time used: 3.675 (sec). Leaf size: 33
DSolve[(3*x+3*y[x]-4)*y'[x]==-(x+y[x]),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*}