29.11.8 problem 299

Internal problem ID [4899]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 299
Date solved : Monday, January 27, 2025 at 09:46:58 AM
CAS classification : [_separable]

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+x y \left (1-y\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve((x^2+1)*diff(y(x),x)+x*y(x)*(1-y(x)) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {1}{1+\sqrt {x^{2}+1}\, c_{1}} \]

✓ Solution by Mathematica

Time used: 2.083 (sec). Leaf size: 33

DSolve[(1+x^2)D[y[x],x]+x y[x](1-y[x])==0,y[x],x,IncludeSingularSolutions -> True]
 

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