Internal problem ID [2920]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 6
Problem number: 172.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } x +\left (-y x +1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 17
dsolve(x*diff(y(x),x)+(1-x*y(x))*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {1}{\left (\ln \relax (x )-c_{1}\right ) x} \]
✓ Solution by Mathematica
Time used: 0.134 (sec). Leaf size: 22
DSolve[x y'[x]+(1-x y[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{-x \log (x)+c_1 x} \\ y(x)\to 0 \\ \end{align*}