78.1.44 problem 4 (f)

Internal problem ID [18099]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 4 (f)
Date solved : Tuesday, January 28, 2025 at 11:26:18 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.360 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 5.645 (sec). Leaf size: 20

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

\[ y(x)\to -W\left (-\frac {e^{-x}}{x}\right )-1 \]