29.11.9 problem 300

Internal problem ID [4900]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 300
Date solved : Monday, January 27, 2025 at 09:47:01 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve((-x^2+1)*diff(y(x),x) = x*y(x)*(1+a*y(x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 3.833 (sec). Leaf size: 47

DSolve[(1-x^2)D[y[x],x]==x y[x](1+a y[x]),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*}