90.1.25 problem 36

Internal problem ID [25049]
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 : 36
Date solved : Thursday, October 02, 2025 at 11:47:52 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 15

ode:=diff(y(t),t) = exp(2*t)-1; 
ic:=[y(0) = 4]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {{\mathrm e}^{2 t}}{2}-t +\frac {7}{2} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 19

ode=D[y[t],{t,1}]== Exp[2*t]-1; 
ic={y[0]==4}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{2} \left (-2 t+e^{2 t}+7\right ) \end{align*}

✓ Sympy. Time used: 0.086 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-exp(2*t) + Derivative(y(t), t) + 1,0) 
ics = {y(0): 4} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - t + \frac {e^{2 t}}{2} + \frac {7}{2} \]