76.5.4 problem 4

Internal problem ID [17424]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 10:07:10 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

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

\[ y = \frac {x -1}{c_{1} x +1} \]

✓ Solution by Mathematica

Time used: 0.320 (sec). Leaf size: 57

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

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1] (K[1]+1)}dK[1]\&\right ]\left [\int _1^x\frac {1}{(K[2]-1) K[2]}dK[2]+c_1\right ] \\ y(x)\to -1 \\ y(x)\to 0 \\ \end{align*}