10.1.27 problem 27

Internal problem ID [1124]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 27
Date solved : Saturday, March 29, 2025 at 10:40:29 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=-1 \end{align*}

✓ Maple. Time used: 0.027 (sec). Leaf size: 19

ode:=1/2*y(t)+diff(y(t),t) = 2*cos(t); 
ic:=y(0) = -1; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \frac {4 \cos \left (t \right )}{5}+\frac {8 \sin \left (t \right )}{5}-\frac {9 \,{\mathrm e}^{-\frac {t}{2}}}{5} \]

✓ Mathematica. Time used: 0.046 (sec). Leaf size: 27

ode=1/2*y[t]+D[y[t],t] == 2*Cos[t]; 
ic=y[0]==-1; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {1}{5} \left (-9 e^{-t/2}+8 \sin (t)+4 \cos (t)\right ) \]

✓ Sympy. Time used: 0.132 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t)/2 - 2*cos(t) + Derivative(y(t), t),0) 
ics = {y(0): -1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {8 \sin {\left (t \right )}}{5} + \frac {4 \cos {\left (t \right )}}{5} - \frac {9 e^{- \frac {t}{2}}}{5} \]