Internal problem ID [4969]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page
7
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x y^{\prime }+y-y^{2}=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (1) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 9
dsolve([x*diff(y(x),x)+y(x)=y(x)^2,y(1) = 1/2],y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{x +1} \]
✓ Solution by Mathematica
Time used: 0.296 (sec). Leaf size: 10
DSolve[{x*y'[x]+y[x]==y[x]^2,{y[1]==1/2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{x+1} \\ \end{align*}