Internal problem ID [946]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-2 y+y^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve([diff(y(x),x)=2*y(x)-y(x)^2,y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {2}{1+{\mathrm e}^{-2 x}} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 9
DSolve[{y'[x]==2*y[x]-y[x]^2,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \tanh (x)+1 \\ \end{align*}