Internal problem ID [3048]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 11
Problem number: 300.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (1-x^{2}\right ) y^{\prime }-x y \left (1+a y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve((-x^2+1)*diff(y(x),x) = x*y(x)*(1+a*y(x)),y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{\sqrt {x -1}\, \sqrt {x +1}\, c_{1}-a} \]
✓ Solution by Mathematica
Time used: 3.99 (sec). Leaf size: 43
DSolve[(1-x^2)y'[x]==x y[x](1+a y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{-a+e^{-c_1} \sqrt {1-x^2}} \\ y(x)\to 0 \\ y(x)\to -\frac {1}{a} \\ \end{align*}