Internal problem ID [3471]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 215.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x y^{\prime }-\ln \left (y\right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 8
dsolve(x*diff(y(x),x) = y(x)*ln(y(x)),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{c_{1} x} \]
✓ Solution by Mathematica
Time used: 0.18 (sec). Leaf size: 18
DSolve[x y'[x]==y[x] Log[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{e^{c_1} x} y(x)\to 1 \end{align*}