Internal problem ID [2881]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 5
Problem number: 132.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+y \ln \relax (x ) \ln \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 16
dsolve(diff(y(x),x)+y(x)*ln(x)*ln(y(x)) = 0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\frac {x^{-x} {\mathrm e}^{x}}{c_{1}}} \]
✓ Solution by Mathematica
Time used: 0.197 (sec). Leaf size: 24
DSolve[y'[x]+y[x] Log[x] Log[y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{x^{-x} e^{x+c_1}} \\ y(x)\to 1 \\ \end{align*}