69.6.34 problem 167

Internal problem ID [18077]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 167
Date solved : Sunday, October 12, 2025 at 05:33:49 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Maple. Time used: 0.027 (sec). Leaf size: 11

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

\[ y = {\mathrm e}^{{\mathrm e}^{x} \left (c_1 +x \right )} \]

✓ Mathematica. Time used: 0.233 (sec). Leaf size: 15

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

\begin{align*} y(x)&\to e^{e^x (x+c_1)} \end{align*}

✓ Sympy. Time used: 0.403 (sec). Leaf size: 14

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

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