8.12 problem 217

Internal problem ID [2965]

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]]

Solve \begin {gather*} \boxed {y^{\prime } x +\left (1-\ln \relax (x )-\ln \relax (y)\right ) y=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 12

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

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

Solution by Mathematica

Time used: 0.206 (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*}