4.1.21 problem 21

Internal problem ID [1118]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 21
Date solved : Tuesday, September 30, 2025 at 04:22:18 AM
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 )&=a \\ \end{align*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 31

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

\begin{align*} y(t)&\to \frac {1}{5} \left ((5 a+4) e^{t/2}+8 \sin (t)-4 \cos (t)\right ) \end{align*}

✓ Sympy. Time used: 0.123 (sec). Leaf size: 26

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

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