60.1.342 problem 343

Internal problem ID [10356]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 343
Date solved : Monday, January 27, 2025 at 07:30:26 PM
CAS classification : [[_1st_order, _with_exponential_symmetries]]

\begin{align*} \left (\ln \left (y\right )+x \right ) y^{\prime }-1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.061 (sec). Leaf size: 27

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

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (-x -\textit {\_Z} -{\mathrm e}^{{\mathrm e}^{\textit {\_Z}}} \operatorname {Ei}_{1}\left ({\mathrm e}^{\textit {\_Z}}\right )+c_{1} {\mathrm e}^{{\mathrm e}^{\textit {\_Z}}}\right )} \]

✓ Solution by Mathematica

Time used: 0.144 (sec). Leaf size: 36

DSolve[-1 + (x + Log[y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x=e^{y(x)} \int _1^{y(x)}e^{-K[1]} \log (K[1])dK[1]+c_1 e^{y(x)},y(x)\right ] \]