Internal problem ID [3473]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 217.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`]]
\[ \boxed {x y^{\prime }+\left (1-\ln \left (x \right )-\ln \left (y\right )\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.232 (sec). Leaf size: 26
DSolve[x y'[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*}