32.2.2 problem Differential equations with Linear Coefficients. Exercise 8.2, page 69

Internal problem ID [5786]
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 8.2, page 69
Date solved : Monday, January 27, 2025 at 01:17:58 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.043 (sec). Leaf size: 21

dsolve((3*x+2*y(x)+1)-(3*x+2*y(x)-1)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {3 x}{2}-\frac {2 \operatorname {LambertW}\left (-\frac {c_{1} {\mathrm e}^{\frac {1}{4}-\frac {25 x}{4}}}{4}\right )}{5}+\frac {1}{10} \]

✓ Solution by Mathematica

Time used: 4.144 (sec). Leaf size: 43

DSolve[(3*x+2*y[x]+1)-(3*x+2*y[x]-1)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{10} \left (-4 W\left (-e^{-\frac {25 x}{4}-1+c_1}\right )-15 x+1\right ) \\ y(x)\to \frac {1}{10}-\frac {3 x}{2} \\ \end{align*}