67.4.13 problem Problem 2(m)

Internal problem ID [13986]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 5.6 Laplace transform. Nonhomogeneous equations. Problems page 368
Problem number : Problem 2(m)
Date solved : Monday, March 31, 2025 at 08:20:53 AM
CAS classification : [[_linear, `class A`]]

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

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.077 (sec). Leaf size: 8

ode:=diff(y(t),t)-y(t) = exp(2*t); 
ic:=y(0) = 1; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = {\mathrm e}^{2 t} \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 10

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

\[ y(t)\to e^{2 t} \]

✓ Sympy. Time used: 0.138 (sec). Leaf size: 7

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

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