72.8.12 problem 25

Internal problem ID [14705]
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 : 25
Date solved : Monday, March 31, 2025 at 12:54:33 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=-5 y+\sin \left (3 t \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=diff(y(t),t) = -5*y(t)+sin(3*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = -\frac {3 \cos \left (3 t \right )}{34}+\frac {5 \sin \left (3 t \right )}{34}+{\mathrm e}^{-5 t} c_1 \]

✓ Mathematica. Time used: 0.087 (sec). Leaf size: 33

ode=D[y[t],t]==-5*y[t]+Sin[3*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-5 t} \left (\int _1^te^{5 K[1]} \sin (3 K[1])dK[1]+c_1\right ) \]

✓ Sympy. Time used: 0.158 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(5*y(t) - sin(3*t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- 5 t} + \frac {5 \sin {\left (3 t \right )}}{34} - \frac {3 \cos {\left (3 t \right )}}{34} \]