Internal problem ID [4007]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli
Equations
Problem number: Exercise 11.22, page 97.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {y}{x}-\frac {y^{2}}{x}=0} \end {gather*} With initial conditions \begin {align*} [y \left (-1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 5
dsolve([diff(y(x),x)+y(x)/x=y(x)^2/x,y(-1) = 1],y(x), singsol=all)
\[ y \relax (x ) = 1 \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 6
DSolve[{y'[x]+y[x]/x==y[x]^2/x,{y[-1]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1 \\ \end{align*}