Internal problem ID [2921]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 6
Problem number: 173.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } x -\left (-y x +1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(x*diff(y(x),x) = (1-x*y(x))*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {2 x}{x^{2}+2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.144 (sec). Leaf size: 23
DSolve[x y'[x]==(1-x y[x])y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 x}{x^2+2 c_1} \\ y(x)\to 0 \\ \end{align*}