72.6.10 problem 10

Internal problem ID [14656]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.8 page 121
Problem number : 10
Date solved : Thursday, March 13, 2025 at 04:12:51 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Maple. Time used: 0.014 (sec). Leaf size: 23

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

\[ y = \frac {3 \cos \left (2 t \right )}{13}+\frac {2 \sin \left (2 t \right )}{13}-\frac {16 \,{\mathrm e}^{-3 t}}{13} \]

✓ Mathematica. Time used: 0.042 (sec). Leaf size: 32

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

\[ y(t)\to e^{-3 t} \left (\int _0^te^{3 K[1]} \cos (2 K[1])dK[1]-1\right ) \]

✓ Sympy. Time used: 0.156 (sec). Leaf size: 27

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(3*y(t) - cos(2*t) + Derivative(y(t), t),0) 
ics = {y(0): -1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {2 \sin {\left (2 t \right )}}{13} + \frac {3 \cos {\left (2 t \right )}}{13} - \frac {16 e^{- 3 t}}{13} \]