66.16.28 problem 29

Internal problem ID [16211]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 4. Forcing and Resonance. Section 4.1 page 399
Problem number : 29
Date solved : Thursday, October 02, 2025 at 10:43:39 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+9 y&=6 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.036 (sec). Leaf size: 12

ode:=diff(diff(y(t),t),t)+9*y(t) = 6; 
ic:=[y(0) = 0, D(y)(0) = 0]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {2}{3}-\frac {2 \cos \left (3 t \right )}{3} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 17

ode=D[y[t],{t,2}]+9*y[t]==6; 
ic={y[0]==0,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {4}{3} \sin ^2\left (\frac {3 t}{2}\right ) \end{align*}

✓ Sympy. Time used: 0.048 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(9*y(t) + Derivative(y(t), (t, 2)) - 6,0) 
ics = {y(0): 0, Subs(Derivative(y(t), t), t, 0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {2}{3} - \frac {2 \cos {\left (3 t \right )}}{3} \]