29.18.17 problem 493

Internal problem ID [5091]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 493
Date solved : Monday, January 27, 2025 at 10:10:29 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 3 \left (x +2 y\right ) y^{\prime }&=1-x -2 y \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 23

dsolve(3*(x+2*y(x))*diff(y(x),x) = 1-x-2*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = -\operatorname {LambertW}\left (-{\mathrm e}^{-\frac {x}{6}-1+\frac {c_{1}}{6}}\right )-1-\frac {x}{2} \]

✓ Solution by Mathematica

Time used: 3.547 (sec). Leaf size: 39

DSolve[3(x+2 y[x])D[y[x],x]==1-x-2 y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -W\left (-e^{-\frac {x}{6}-1+c_1}\right )-\frac {x}{2}-1 \\ y(x)\to -\frac {x}{2}-1 \\ \end{align*}