74.5.41 problem 48

Internal problem ID [15934]
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 : 48
Date solved : Monday, March 31, 2025 at 02:13:50 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&=5 \,{\mathrm e}^{2 t} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=diff(y(t),t)+y(t) = 5*exp(2*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {5 \,{\mathrm e}^{2 t}}{3}+{\mathrm e}^{-t} c_1 \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 23

ode=D[y[t],t]+y[t]==5*Exp[2*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {5 e^{2 t}}{3}+c_1 e^{-t} \]

✓ Sympy. Time used: 0.132 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t) - 5*exp(2*t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- t} + \frac {5 e^{2 t}}{3} \]