Internal problem ID [12145]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 67.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime }-y x +a x y^{2}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve((1-x^2)*diff(y(x),x)-x*y(x)+a*x*y(x)^2=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{\sqrt {x -1}\, \sqrt {x +1}\, c_{1} +a} \]
✓ Solution by Mathematica
Time used: 4.118 (sec). Leaf size: 35
DSolve[(1-x^2)*y'[x]-x*y[x]+a*x*y[x]^2==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*}