29.6.27 problem 173

Internal problem ID [4773]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 6
Problem number : 173
Date solved : Monday, January 27, 2025 at 09:37:14 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

dsolve(x*diff(y(x),x) = (1-x*y(x))*y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.148 (sec). Leaf size: 23

DSolve[x D[y[x],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*}