4.1.29 problem 29

Internal problem ID [1126]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 29
Date solved : Tuesday, September 30, 2025 at 04:23:09 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} \frac {y}{4}+y^{\prime }&=3+2 \cos \left (2 t \right ) \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.023 (sec). Leaf size: 24

ode:=1/4*y(t)+diff(y(t),t) = 3+2*cos(2*t); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = 12+\frac {8 \cos \left (2 t \right )}{65}+\frac {64 \sin \left (2 t \right )}{65}-\frac {788 \,{\mathrm e}^{-\frac {t}{4}}}{65} \]

✓ Mathematica. Time used: 0.098 (sec). Leaf size: 32

ode=1/4*y[t]+D[y[t],t] == 3+2*Cos[2*t]; 
ic=y[0]==0; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {4}{65} \left (-197 e^{-t/4}+16 \sin (2 t)+2 \cos (2 t)+195\right ) \end{align*}

✓ Sympy. Time used: 0.469 (sec). Leaf size: 29

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t)/4 - 2*cos(2*t) + Derivative(y(t), t) - 3,0) 
ics = {y(0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {64 \sin {\left (2 t \right )}}{65} + \frac {8 \cos {\left (2 t \right )}}{65} + 12 - \frac {788 e^{- \frac {t}{4}}}{65} \]