72.8.10 problem 23

Internal problem ID [14695]
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. Review Exercises for chapter 1. page 136
Problem number : 23
Date solved : Thursday, March 13, 2025 at 04:15:15 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=3 y+{\mathrm e}^{7 t} \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 18

ode:=diff(y(t),t) = 3*y(t)+exp(7*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {\left ({\mathrm e}^{4 t}+4 c_{1} \right ) {\mathrm e}^{3 t}}{4} \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 23

ode=D[y[t],t]==3*y[t]+Exp[7*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {e^{7 t}}{4}+c_1 e^{3 t} \]

✓ Sympy. Time used: 0.147 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-3*y(t) - exp(7*t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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