Internal problem ID [3047]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 11
Problem number: 299.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime }+x y \left (1-y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 17
dsolve((x^2+1)*diff(y(x),x)+x*y(x)*(1-y(x)) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{1+\sqrt {x^{2}+1}\, c_{1}} \]
✓ Solution by Mathematica
Time used: 0.378 (sec). Leaf size: 33
DSolve[(1+x^2)y'[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*}