32.2.8 problem Differential equations with Linear Coefficients. Exercise 8.8, page 69

Internal problem ID [5792]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 8
Problem number : Differential equations with Linear Coefficients. Exercise 8.8, page 69
Date solved : Monday, January 27, 2025 at 01:18:11 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x +2 y+\left (3 x +6 y+3\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 23

dsolve((x+2*y(x))+(3*x+6*y(x)+3)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-\frac {x}{6}-\frac {3}{2}+\frac {c_{1}}{6}}}{2}\right )-\frac {3}{2}-\frac {x}{2} \]

✓ Solution by Mathematica

Time used: 4.624 (sec). Leaf size: 43

DSolve[(x+2*y[x])+(3*x+6*y[x]+3)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{2} \left (-2 W\left (-e^{-\frac {x}{6}-1+c_1}\right )-x-3\right ) \\ y(x)\to \frac {1}{2} (-x-3) \\ \end{align*}