23.1.21 problem 2(k)

Internal problem ID [4111]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 2. First order equations. Exercises at page 14
Problem number : 2(k)
Date solved : Monday, January 27, 2025 at 08:09:11 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 )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.173 (sec). Leaf size: 21

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

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

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

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