66.19.1 problem 27

Internal problem ID [16246]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 6. Laplace transform. Section 6.3 page 600
Problem number : 27
Date solved : Thursday, October 02, 2025 at 10:44:04 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+4 y&=8 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=11 \\ y^{\prime }\left (0\right )&=5 \\ \end{align*}

✓ Maple. Time used: 0.126 (sec). Leaf size: 18

ode:=diff(diff(y(t),t),t)+4*y(t) = 8; 
ic:=[y(0) = 11, D(y)(0) = 5]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = 2+9 \cos \left (2 t \right )+\frac {5 \sin \left (2 t \right )}{2} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 19

ode=D[y[t],{t,2}]+4*y[t]==8; 
ic={y[0]==11,Derivative[1][y][0] ==5}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 9 \cos (2 t)+5 \sin (t) \cos (t)+2 \end{align*}

✓ Sympy. Time used: 0.046 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*y(t) + Derivative(y(t), (t, 2)) - 8,0) 
ics = {y(0): 11, Subs(Derivative(y(t), t), t, 0): 5} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {5 \sin {\left (2 t \right )}}{2} + 9 \cos {\left (2 t \right )} + 2 \]