Internal problem ID [883]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 1, Introduction. Section 1.2 Page 14
Problem number: 5(d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {y \left (1+y\right )}{x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = -2] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 11
dsolve([diff(y(x),x) = (- y(x)*(y(x)+1))/x,y(1) = -2],y(x), singsol=all)
\[ y \relax (x ) = \frac {2}{-2+x} \]
✓ Solution by Mathematica
Time used: 0.226 (sec). Leaf size: 12
DSolve[{y'[x] ==(- y[x]*(y[x]+1))/x,y[1]==-2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2}{x-2} \\ \end{align*}