66.6.5 problem 5

Internal problem ID [16017]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.8 page 121
Problem number : 5
Date solved : Thursday, October 02, 2025 at 10:38:54 AM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

\[ y = \left (-4 t +c_1 \right ) {\mathrm e}^{3 t} \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 17

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

\begin{align*} y(t)&\to e^{3 t} (-4 t+c_1) \end{align*}

✓ Sympy. Time used: 0.082 (sec). Leaf size: 12

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

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