72.6.9 problem 9

Internal problem ID [14663]
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 : 9
Date solved : Monday, March 31, 2025 at 12:51:56 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=5 \end{align*}

✓ Maple. Time used: 0.023 (sec). Leaf size: 23

ode:=diff(y(t),t)+y(t) = cos(2*t); 
ic:=y(0) = 5; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \frac {\cos \left (2 t \right )}{5}+\frac {2 \sin \left (2 t \right )}{5}+\frac {24 \,{\mathrm e}^{-t}}{5} \]

✓ Mathematica. Time used: 0.055 (sec). Leaf size: 30

ode=D[y[t],t]+y[t]==Cos[2*t]; 
ic={y[0]==5}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-t} \left (\int _0^te^{K[1]} \cos (2 K[1])dK[1]+5\right ) \]

✓ Sympy. Time used: 0.147 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t) - cos(2*t) + Derivative(y(t), t),0) 
ics = {y(0): 5} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {2 \sin {\left (2 t \right )}}{5} + \frac {\cos {\left (2 t \right )}}{5} + \frac {24 e^{- t}}{5} \]