Internal problem ID [3865]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 2
Problem number: 10.1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (1-x^{2}\right ) z^{\prime }-x z-a x z^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve((1-x^2)*diff(z(x),x)-x*z(x)=a*x*z(x)^2,z(x), singsol=all)
\[ z \relax (x ) = \frac {1}{\sqrt {x -1}\, \sqrt {x +1}\, c_{1}-a} \]
✓ Solution by Mathematica
Time used: 4.031 (sec). Leaf size: 43
DSolve[(1-x^2)*z'[x]-x*z[x]==a*x*z[x]^2,z[x],x,IncludeSingularSolutions -> True]
\begin{align*} z(x)\to \frac {1}{-a+e^{-c_1} \sqrt {1-x^2}} \\ z(x)\to 0 \\ z(x)\to -\frac {1}{a} \\ \end{align*}