Internal problem ID [3556]
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]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime }-x y \left (1+a y\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve((-x^2+1)*diff(y(x),x) = x*y(x)*(1+a*y(x)),y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{\sqrt {x -1}\, \sqrt {x +1}\, c_{1} -a} \]
✓ Solution by Mathematica
Time used: 3.979 (sec). Leaf size: 47
DSolve[(1-x^2)y'[x]==x y[x](1+a y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {e^{c_1}}{-\sqrt {1-x^2}+a e^{c_1}} y(x)\to 0 y(x)\to -\frac {1}{a} \end{align*}