Internal problem ID [7923]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 343.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_exponential_symmetries]]
Solve \begin {gather*} \boxed {\left (\ln \relax (y)+x \right ) y^{\prime }-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.235 (sec). Leaf size: 27
dsolve((ln(y(x))+x)*diff(y(x),x)-1 = 0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left (-x -\textit {\_Z} -\expIntegral \left (1, {\mathrm e}^{\textit {\_Z}}\right ) {\mathrm e}^{{\mathrm e}^{\textit {\_Z}}}+c_{1} {\mathrm e}^{{\mathrm e}^{\textit {\_Z}}}\right )} \]
✓ Solution by Mathematica
Time used: 0.216 (sec). Leaf size: 35
DSolve[-1 + (x + Log[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=e^{y(x)} \left (\text {Ei}(-y(x))-e^{-y(x)} \log (y(x))\right )+c_1 e^{y(x)},y(x)\right ] \]