74.5.51 problem 58

Internal problem ID [15936]
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 : 58
Date solved : Thursday, March 13, 2025 at 06:58:01 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&=4+3 \,{\mathrm e}^{t} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=diff(y(t),t)+y(t) = 4+3*exp(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = 4+\frac {3 \,{\mathrm e}^{t}}{2}+{\mathrm e}^{-t} c_{1} \]

✓ Mathematica. Time used: 0.066 (sec). Leaf size: 26

ode=D[y[t],t]+y[t]==4+3*Exp[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {3 e^t}{2}+\left (\frac {8}{3}+c_1\right ) e^{-t}+4 \]

✓ Sympy. Time used: 0.146 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t) - 3*exp(t) + Derivative(y(t), t) - 4,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- t} + \frac {3 e^{t}}{2} + 4 \]