68.4.17 problem 17

Internal problem ID [17197]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 17
Date solved : Thursday, October 02, 2025 at 01:51:01 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&={\mathrm e}^{3 y+2 t} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 26

ode:=diff(y(t),t) = exp(3*y(t)+2*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = -\frac {\ln \left (3\right )}{3}+\frac {\ln \left (2\right )}{3}-\frac {\ln \left (-{\mathrm e}^{2 t}-2 c_1 \right )}{3} \]

✓ Mathematica. Time used: 0.675 (sec). Leaf size: 24

ode=D[y[t],t]==Exp[3*y[t]+2*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\frac {1}{3} \log \left (-\frac {3}{2} \left (e^{2 t}+2 c_1\right )\right ) \end{align*}

✓ Sympy. Time used: 1.282 (sec). Leaf size: 99

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-exp(2*t + 3*y(t)) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = \frac {\log {\left (- \frac {1}{C_{1} + 3 e^{2 t}} \right )}}{3} + \frac {\log {\left (2 \right )}}{3}, \ y{\left (t \right )} = \log {\left (\frac {\sqrt [3]{2} \sqrt [3]{- \frac {1}{C_{1} + e^{2 t}}} \left (- 3^{\frac {2}{3}} - 3 \sqrt [6]{3} i\right )}{6} \right )}, \ y{\left (t \right )} = \log {\left (\frac {\sqrt [3]{2} \sqrt [3]{- \frac {1}{C_{1} + e^{2 t}}} \left (- 3^{\frac {2}{3}} + 3 \sqrt [6]{3} i\right )}{6} \right )}\right ] \]