60.2.69 problem 645

Internal problem ID [10643]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 645
Date solved : Wednesday, March 05, 2025 at 12:13:54 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.067 (sec). Leaf size: 14

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

\[ y = {\mathrm e}^{c_{1} {\mathrm e}^{-x}-1+x} \]

✓ Mathematica. Time used: 0.275 (sec). Leaf size: 20

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

\[ y(x)\to e^{x-e^{-x+c_1}-1} \]

✓ Sympy. Time used: 0.768 (sec). Leaf size: 12

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

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