Internal problem ID [11193]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 19.
Summary. Page 29
Problem number: Ex 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime }-y x -y^{2} a x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve((1-x^2)*diff(y(x),x)-x*y(x)=a*x*y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{\sqrt {x -1}\, \sqrt {x +1}\, c_{1} -a} \]
✓ Solution by Mathematica
Time used: 4.13 (sec). Leaf size: 47
DSolve[(1-x^2)*y'[x]-x*y[x]==a*x*y[x]^2,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*}