Internal problem ID [2835]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 3
Problem number: 80.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-y \left (a +b y^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 70
dsolve(diff(y(x),x) = y(x)*(a+b*y(x)^2),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {\left (c_{1} a \,{\mathrm e}^{-2 a x}-b \right ) a}}{c_{1} a \,{\mathrm e}^{-2 a x}-b} \\ y \relax (x ) = -\frac {\sqrt {\left (c_{1} a \,{\mathrm e}^{-2 a x}-b \right ) a}}{c_{1} a \,{\mathrm e}^{-2 a x}-b} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.564 (sec). Leaf size: 118
DSolve[y'[x]==y[x](a+b y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i \sqrt {a} e^{a (x+c_1)}}{\sqrt {-1+b e^{2 a (x+c_1)}}} \\ y(x)\to \frac {i \sqrt {a} e^{a (x+c_1)}}{\sqrt {-1+b e^{2 a (x+c_1)}}} \\ y(x)\to 0 \\ y(x)\to -\frac {i \sqrt {a}}{\sqrt {b}} \\ y(x)\to \frac {i \sqrt {a}}{\sqrt {b}} \\ \end{align*}