90.1.16 problem 27

Internal problem ID [25040]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 13
Problem number : 27
Date solved : Thursday, October 02, 2025 at 11:47:45 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=diff(y(t),t) = exp(2*t)-1; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {{\mathrm e}^{2 t}}{2}-t +c_1 \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 20

ode=D[y[t],{t,1}]== Exp[2*t]-1; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.083 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-exp(2*t) + Derivative(y(t), t) + 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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