38.2.16 problem 16

Internal problem ID [6445]
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
Date solved : Monday, January 27, 2025 at 02:04:17 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (3 x +3 y-4\right ) y^{\prime }&=-x -y \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 21

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

\[ y = \frac {2 \operatorname {LambertW}\left (\frac {3 \,{\mathrm e}^{x -3-c_1}}{2}\right )}{3}-x +2 \]

✓ Solution by Mathematica

Time used: 3.184 (sec). Leaf size: 33

DSolve[(3*x+3*y[x]-4)*D[y[x],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*}