Internal problem ID [953]
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.
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*} With initial conditions \begin {align*} [y \relax (0) = \mathit {y0}] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 25
dsolve([diff(y(x),x)=a*y(x)-b*y(x)^2,y(0) = y0],y(x), singsol=all)
\[ y \relax (x ) = \frac {a \mathit {y0}}{\left (-\mathit {y0} b +a \right ) {\mathrm e}^{-a x}+\mathit {y0} b} \]
✓ Solution by Mathematica
Time used: 0.683 (sec). Leaf size: 27
DSolve[{y'[x]==a*y[x]-b*y[x]^2,y[0]==y0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {a \text {y0} e^{a x}}{b \text {y0} \left (e^{a x}-1\right )+a} \\ \end{align*}