74.11.51 problem 62 (b)

Internal problem ID [16230]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 62 (b)
Date solved : Monday, March 31, 2025 at 02:47:46 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 )&=0 \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 23

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

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

✓ Mathematica. Time used: 0.062 (sec). Leaf size: 28

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

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

✓ 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): 0} 
dsolve(ode,func=y(t),ics=ics)
 

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