74.5.58 problem 63 (c)

Internal problem ID [15951]
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 : 63 (c)
Date solved : Monday, March 31, 2025 at 02:14:27 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Maple. Time used: 0.028 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.046 (sec). Leaf size: 26

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

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

✓ Sympy. Time used: 0.148 (sec). Leaf size: 19

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

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