15.3.7 problem 7

Internal problem ID [2900]
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 : 7
Date solved : Monday, January 27, 2025 at 06:28:02 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 21

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

\[ y = \frac {\operatorname {LambertW}\left (2 \,{\mathrm e}^{x -2-c_1}\right )}{2}-x +1 \]

✓ Solution by Mathematica

Time used: 3.920 (sec). Leaf size: 33

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