74.5.26 problem 26

Internal problem ID [15911]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 26
Date solved : Thursday, March 13, 2025 at 06:57:06 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-y&=4 \,{\mathrm e}^{t} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.015 (sec). Leaf size: 11

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

\[ y = 4 \left (t +1\right ) {\mathrm e}^{t} \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 13

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

\[ y(t)\to 4 e^t (t+1) \]

✓ Sympy. Time used: 0.134 (sec). Leaf size: 10

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

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