4.1.5 problem 5

Internal problem ID [1102]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 5
Date solved : Tuesday, September 30, 2025 at 04:21:50 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} -2 y+y^{\prime }&=3 \,{\mathrm e}^{t} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=-2*y(t)+diff(y(t),t) = 3*exp(t); 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 17

ode=-2*y[t]+D[y[t],t] == 3*Exp[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^t \left (-3+c_1 e^t\right ) \end{align*}

✓ Sympy. Time used: 0.077 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-2*y(t) - 3*exp(t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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