74.5.3 problem 3

Internal problem ID [15896]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 3
Date solved : Monday, March 31, 2025 at 02:12:14 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.052 (sec). Leaf size: 30

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

\[ y(t)\to e^t \left (\int _1^t2 e^{-K[1]} \cos (K[1])dK[1]+c_1\right ) \]

✓ Sympy. Time used: 0.129 (sec). Leaf size: 14

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

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