60.1.336 problem 343

Internal problem ID [10350]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 343
Date solved : Sunday, March 30, 2025 at 04:22:57 PM
CAS classification : [[_1st_order, _with_exponential_symmetries]]

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

✓ Maple. Time used: 0.022 (sec). Leaf size: 27

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

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (-x -\textit {\_Z} -\operatorname {Ei}_{1}\left ({\mathrm e}^{\textit {\_Z}}\right ) {\mathrm e}^{{\mathrm e}^{\textit {\_Z}}}+{\mathrm e}^{{\mathrm e}^{\textit {\_Z}}} c_1 \right )} \]

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

ode=-1 + (x + Log[y[x]])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 1.625 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + log(y(x)))*Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ C_{1} + x e^{- y{\left (x \right )}} - \operatorname {Ei}{\left (- y{\left (x \right )} \right )} + e^{- y{\left (x \right )}} \log {\left (y{\left (x \right )} \right )} = 0 \]