15.3.8 problem 8

Internal problem ID [2901]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 7, page 28
Problem number : 8
Date solved : Monday, January 27, 2025 at 06:28:04 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 3.880 (sec). Leaf size: 24

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

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