32.2.9 problem Differential equations with Linear Coefficients. Exercise 8.9, page 69

Internal problem ID [5793]
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 8.9, page 69
Date solved : Monday, January 27, 2025 at 01:18:13 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.756 (sec). Leaf size: 30

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

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

✓ Solution by Mathematica

Time used: 1.165 (sec). Leaf size: 143

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

\[ \text {Solve}\left [-\frac {(-2)^{2/3} \left (-\left ((x+1) \log \left (-\frac {3 (-2)^{2/3} (x+2)}{y(x)-1}\right )\right )+x \log \left (\frac {3 (-2)^{2/3} (y(x)+x+1)}{y(x)-1}\right )+\log \left (\frac {3 (-2)^{2/3} (y(x)+x+1)}{y(x)-1}\right )+y(x) \left (-\log \left (-\frac {3 (-2)^{2/3} (x+2)}{y(x)-1}\right )+\log \left (\frac {3 (-2)^{2/3} (y(x)+x+1)}{y(x)-1}\right )-1\right )+1\right )}{9 (y(x)+x+1)}=\frac {1}{9} (-2)^{2/3} \log (x+2)+c_1,y(x)\right ] \]