29.8.12 problem 217

Internal problem ID [4817]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 217
Date solved : Monday, January 27, 2025 at 09:41:12 AM
CAS classification : [[_homogeneous, `class G`]]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.278 (sec). Leaf size: 26

DSolve[x D[y[x],x]+(1-Log[x]-Log[y[x]])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {e^{e^{-c_1} x}}{x} \\ y(x)\to \frac {1}{x} \\ \end{align*}