12.3.26 problem 27

Internal problem ID [1603]
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 : 27
Date solved : Monday, January 27, 2025 at 05:13:34 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=\operatorname {y0} \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 25

dsolve([diff(y(x),x)=a*y(x)-b*y(x)^2,y(0) = y0],y(x), singsol=all)
 

\[ y = \frac {a \operatorname {y0}}{\left (-\operatorname {y0} b +a \right ) {\mathrm e}^{-a x}+\operatorname {y0} b} \]

✓ Solution by Mathematica

Time used: 0.731 (sec). Leaf size: 27

DSolve[{D[y[x],x]==a*y[x]-b*y[x]^2,y[0]==y0},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {a \text {y0} e^{a x}}{b \text {y0} \left (e^{a x}-1\right )+a} \]