Internal problem ID [979]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }+y-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 12
dsolve(diff(y(x),x)+y(x)=y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{1+c_{1} {\mathrm e}^{x}} \]
✓ Solution by Mathematica
Time used: 0.244 (sec). Leaf size: 54
DSolve[y'[x]+y[x]==y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {1+e^{2 (x+c_1)}}} \\ y(x)\to \frac {1}{\sqrt {1+e^{2 (x+c_1)}}} \\ y(x)\to -1 \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}