72.6.16 problem 24

Internal problem ID [14670]
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 : 24
Date solved : Monday, March 31, 2025 at 12:52:14 PM
CAS classification : [[_linear, `class A`]]

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

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

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

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

✓ Mathematica. Time used: 0.101 (sec). Leaf size: 44

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

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

✓ Sympy. Time used: 0.214 (sec). Leaf size: 19

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

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