Internal problem ID [4373]
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]
\[ \boxed {\left (-x^{2}+1\right ) z^{\prime }-x z-a x z^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve((1-x^2)*diff(z(x),x)-x*z(x)=a*x*z(x)^2,z(x), singsol=all)
\[ z \left (x \right ) = \frac {1}{\sqrt {x -1}\, \sqrt {1+x}\, c_{1} -a} \]
✓ Solution by Mathematica
Time used: 3.943 (sec). Leaf size: 47
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 {e^{c_1}}{-\sqrt {1-x^2}+a e^{c_1}} \\ z(x)\to 0 \\ z(x)\to -\frac {1}{a} \\ \end{align*}