74.8.9 problem 9

Internal problem ID [16066]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 9
Date solved : Thursday, March 13, 2025 at 07:38:37 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+3 y&=-10 \sin \left (t \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=diff(y(t),t)+3*y(t) = -10*sin(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \cos \left (t \right )-3 \sin \left (t \right )+{\mathrm e}^{-3 t} c_{1} \]

✓ Mathematica. Time used: 0.054 (sec). Leaf size: 32

ode=D[y[t],t]+3*y[t]==-10*Sin[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-3 t} \left (\int _1^t-10 e^{3 K[1]} \sin (K[1])dK[1]+c_1\right ) \]

✓ Sympy. Time used: 0.135 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(3*y(t) + 10*sin(t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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