90.4.3 problem 3

Internal problem ID [25098]
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 59
Problem number : 3
Date solved : Thursday, October 02, 2025 at 11:50:09 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 12

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

\[ y = \left (t +4\right ) {\mathrm e}^{2 t} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 14

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

\begin{align*} y(t)&\to e^{2 t} (t+4) \end{align*}

✓ Sympy. Time used: 0.083 (sec). Leaf size: 10

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

\[ y{\left (t \right )} = \left (t + 4\right ) e^{2 t} \]