72.5.24 problem 11

Internal problem ID [14631]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.6 page 89
Problem number : 11
Date solved : Thursday, March 13, 2025 at 04:11:06 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.274 (sec). Leaf size: 21

ode:=diff(y(t),t) = y(t)*ln(abs(y(t))); 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= {\mathrm e}^{-c_{1} {\mathrm e}^{t}} \\ y &= -{\mathrm e}^{-c_{1} {\mathrm e}^{t}} \\ \end{align*}

✓ Mathematica. Time used: 0.221 (sec). Leaf size: 35

ode=D[y[t],t]==y[t]*Log[Abs[y[t]]]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1] \log (| K[1]| )}dK[1]\&\right ][t+c_1] \\ y(t)\to 1 \\ \end{align*}

✓ Sympy. Time used: 0.286 (sec). Leaf size: 14

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

\[ \int \limits ^{y{\left (t \right )}} \frac {1}{y \log {\left (\left |{y}\right | \right )}}\, dy = C_{1} + t \]