Internal problem ID [532]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.5. Page 88
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-a y-b y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve(diff(y(x),x) = a*y(x)+b*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {a}{{\mathrm e}^{-a x} c_{1} a -b} \]
✓ Solution by Mathematica
Time used: 0.656 (sec). Leaf size: 38
DSolve[y'[x]== a*y[x]+b*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {a}{b-e^{-a (x+c_1)}} \\ y(x)\to 0 \\ y(x)\to -\frac {a}{b} \\ \end{align*}