68.4.16 problem 16

Internal problem ID [17196]
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 : 16
Date solved : Thursday, October 02, 2025 at 01:51:00 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&={\mathrm e}^{2 y+10 t} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 22

ode:=diff(y(t),t) = exp(2*y(t)+10*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {\ln \left (5\right )}{2}-\frac {\ln \left (-{\mathrm e}^{10 t}-10 c_1 \right )}{2} \]

✓ Mathematica. Time used: 0.708 (sec). Leaf size: 24

ode=D[y[t],t]==Exp[2*y[t]+10*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\frac {1}{2} \log \left (-\frac {e^{10 t}}{5}-2 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.310 (sec). Leaf size: 44

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-exp(10*t + 2*y(t)) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = \log {\left (- \sqrt {- \frac {1}{C_{1} + e^{10 t}}} \right )} + \frac {\log {\left (5 \right )}}{2}, \ y{\left (t \right )} = \frac {\log {\left (- \frac {1}{C_{1} + e^{10 t}} \right )}}{2} + \frac {\log {\left (5 \right )}}{2}\right ] \]