32.2.4 problem Differential equations with Linear Coefficients. Exercise 8.4, page 69

Internal problem ID [5788]
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 8.4, page 69
Date solved : Monday, January 27, 2025 at 01:18:01 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.034 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 4.043 (sec). Leaf size: 33

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

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