Internal problem ID [13324]
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: 4.6 (f).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-200 y+2 y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(y(x),x)=200*y(x)-2*y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {100}{1+100 \,{\mathrm e}^{-200 x} c_{1}} \]
✓ Solution by Mathematica
Time used: 0.285 (sec). Leaf size: 36
DSolve[y'[x]==200*y[x]-2*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {100 e^{200 x}}{e^{200 x}+e^{100 c_1}} \\ y(x)\to 0 \\ y(x)\to 100 \\ \end{align*}