Internal problem ID [8225]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 645.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime }-\left (-\ln \relax (y)+x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.126 (sec). Leaf size: 14
dsolve(diff(y(x),x) = (-ln(y(x))+x)*y(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{{\mathrm e}^{-x} c_{1}-1+x} \]
✓ Solution by Mathematica
Time used: 0.27 (sec). Leaf size: 20
DSolve[y'[x] == (x - Log[y[x]])*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{x-e^{-x+c_1}-1} \\ \end{align*}