29.6.26 problem 172

Internal problem ID [4772]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 6
Problem number : 172
Date solved : Monday, January 27, 2025 at 09:37:12 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

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

\[ y \left (x \right ) = \frac {1}{\left (c_{1} -\ln \left (x \right )\right ) x} \]

✓ Solution by Mathematica

Time used: 0.140 (sec). Leaf size: 22

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