10.4.1 problem 1

Internal problem ID [1182]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.5. Page 88
Problem number : 1
Date solved : Monday, January 27, 2025 at 04:39:37 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve(diff(y(x),x) = a*y(x)+b*y(x)^2,y(x), singsol=all)
 

\[ y = \frac {a}{{\mathrm e}^{-a x} c_1 a -b} \]

✓ Solution by Mathematica

Time used: 0.729 (sec). Leaf size: 45

DSolve[D[y[x],x]== a*y[x]+b*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {a e^{a (x+c_1)}}{-1+b e^{a (x+c_1)}} \\ y(x)\to 0 \\ y(x)\to -\frac {a}{b} \\ \end{align*}