12.13 problem Ex 14

Internal problem ID [10169]

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]

Solve \begin {gather*} \boxed {\left (-x^{2}+1\right ) y^{\prime }-y x -a x y^{2}=0} \end {gather*}

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)
 

\[ y \relax (x ) = \frac {1}{\sqrt {x -1}\, \sqrt {1+x}\, c_{1}-a} \]

Solution by Mathematica

Time used: 4.086 (sec). Leaf size: 43

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 {1}{-a+e^{-c_1} \sqrt {1-x^2}} \\ y(x)\to 0 \\ y(x)\to -\frac {1}{a} \\ \end{align*}