72.6.3 problem 3

Internal problem ID [14657]
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 : 3
Date solved : Monday, March 31, 2025 at 12:51:43 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=-3 y+4 \cos \left (2 t \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

ode:=diff(y(t),t) = -3*y(t)+4*cos(2*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {12 \cos \left (2 t \right )}{13}+\frac {8 \sin \left (2 t \right )}{13}+{\mathrm e}^{-3 t} c_1 \]

✓ Mathematica. Time used: 0.09 (sec). Leaf size: 34

ode=D[y[t],t]==-3*y[t]+4*Cos[2*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-3 t} \left (\int _1^t4 e^{3 K[1]} \cos (2 K[1])dK[1]+c_1\right ) \]

✓ Sympy. Time used: 0.154 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(3*y(t) - 4*cos(2*t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- 3 t} + \frac {8 \sin {\left (2 t \right )}}{13} + \frac {12 \cos {\left (2 t \right )}}{13} \]