Internal problem ID [7738]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 158.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x^{2}-1\right ) y^{\prime }+a x y^{2}+y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 22
dsolve((x^2-1)*diff(y(x),x) + a*x*y(x)^2 + x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{\sqrt {x -1}\, \sqrt {x +1}\, c_{1}-a} \]
✓ Solution by Mathematica
Time used: 0.603 (sec). Leaf size: 41
DSolve[(x^2-1)*y'[x] + a*x*y[x]^2 + x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{-a+e^{-c_1} \sqrt {x^2-1}} \\ y(x)\to 0 \\ y(x)\to -\frac {1}{a} \\ \end{align*}