74.8.7 problem 7

Internal problem ID [16064]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 7
Date solved : Thursday, March 13, 2025 at 07:38:32 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {y \,{\mathrm e}^{-2 t}}{\ln \left (y\right )} \end{align*}

✓ Maple. Time used: 0.116 (sec). Leaf size: 35

ode:=diff(y(t),t) = y(t)/exp(2*t)/ln(y(t)); 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= {\mathrm e}^{\sqrt {2 c_{1} -{\mathrm e}^{-2 t}}} \\ y &= {\mathrm e}^{-\sqrt {2 c_{1} -{\mathrm e}^{-2 t}}} \\ \end{align*}

✓ Mathematica. Time used: 11.16 (sec). Leaf size: 61

ode=D[y[t],t]==y[t]/(Exp[2*t]*Log[y[t]]); 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)\to e^{-e^{-t} \sqrt {-1+2 c_1 e^{2 t}}} \\ y(t)\to e^{e^{-t} \sqrt {-1+2 c_1 e^{2 t}}} \\ y(t)\to 0 \\ \end{align*}

✓ Sympy. Time used: 1.688 (sec). Leaf size: 32

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t)*exp(-2*t)/log(y(t)) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = e^{- \sqrt {C_{1} - e^{- 2 t}}}, \ y{\left (t \right )} = e^{\sqrt {C_{1} - e^{- 2 t}}}\right ] \]