2.16 problem 16

Internal problem ID [4594]

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]]

Solve \begin {gather*} \boxed {\left (3 x +3 y-4\right ) y^{\prime }+x +y=0} \end {gather*}

Solution by Maple

Time used: 0.027 (sec). Leaf size: 29

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

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

Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 24

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} \text {ProductLog}\left (-e^{x-1+c_1}\right )-x+2 \\ \end{align*}