12.3.19 problem 20

Internal problem ID [1596]
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
Date solved : Monday, January 27, 2025 at 05:12:56 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=2 y-y^{2} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=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)
 

\[ y = \frac {2}{1+{\mathrm e}^{-2 x}} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 21

DSolve[{D[y[x],x]==2*y[x]-y[x]^2,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 e^{2 x}}{e^{2 x}+1} \]