83.15.7 problem 4 (g)

Internal problem ID [22031]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter XV. The Laplace Transform. Ex. XXIII at page 251
Problem number : 4 (g)
Date solved : Thursday, October 02, 2025 at 08:21:49 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=5 \cos \left (2 t \right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=2 \\ y^{\prime }\left (0\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.061 (sec). Leaf size: 17

ode:=diff(diff(y(t),t),t)+9*y(t) = 5*cos(2*t); 
ic:=[y(0) = 2, D(y)(0) = 3]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = \cos \left (2 t \right )+\cos \left (3 t \right )+\sin \left (3 t \right ) \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 18

ode=D[y[t],{t,2}]+9*y[t]==5*Cos[2*t]; 
ic={y[0]==2,Derivative[1][y][0] ==3}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \sin (3 t)+\cos (2 t)+\cos (3 t) \end{align*}

✓ Sympy. Time used: 0.047 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(9*y(t) - 5*cos(2*t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 2, Subs(Derivative(y(t), t), t, 0): 3} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \sin {\left (3 t \right )} + \cos {\left (2 t \right )} + \cos {\left (3 t \right )} \]