40.2.9 problem 32

Internal problem ID [6587]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary problems. Page 22
Problem number : 32
Date solved : Monday, January 27, 2025 at 02:14:26 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 19

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

\[ y = \frac {\operatorname {LambertW}\left (2 \,{\mathrm e}^{x -c_1}\right )}{2}-x \]

✓ Solution by Mathematica

Time used: 3.967 (sec). Leaf size: 30

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

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