81.3.10 problem 10

Internal problem ID [18628]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 12:04:42 PM
CAS classification : [_separable]

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-y x&=a x y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.005 (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: 3.763 (sec). Leaf size: 45

DSolve[(1-x^2)*D[y[x],x]-x*y[x]==a*x*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

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