73.3.41 problem 4.7 (o)

Internal problem ID [15075]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.7 (o)
Date solved : Tuesday, January 28, 2025 at 07:29:47 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=200 y-2 y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

dsolve(diff(y(x),x)=200*y(x)-2*y(x)^2,y(x), singsol=all)
 

\[ y = \frac {100}{1+100 \,{\mathrm e}^{-200 x} c_{1}} \]

✓ Solution by Mathematica

Time used: 0.211 (sec). Leaf size: 42

DSolve[D[y[x],x]==200*y[x]-2*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-100) K[1]}dK[1]\&\right ][-2 x+c_1] \\ y(x)\to 0 \\ y(x)\to 100 \\ \end{align*}