46.5.7 problem 37

Internal problem ID [9616]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 7 THE LAPLACE TRANSFORM. 7.2.2 TRANSFORMS OF DERIVATIVES Page 289
Problem number : 37
Date solved : Tuesday, September 30, 2025 at 06:21:30 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=\sqrt {2}\, \sin \left (\sqrt {2}\, t \right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=10 \\ y^{\prime }\left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.115 (sec). Leaf size: 24

ode:=diff(diff(y(t),t),t)+y(t) = 2^(1/2)*sin(2^(1/2)*t); 
ic:=[y(0) = 10, D(y)(0) = 0]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = 10 \cos \left (t \right )+2 \sin \left (t \right )-\sqrt {2}\, \sin \left (\sqrt {2}\, t \right ) \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 29

ode=D[y[t],{t,2}]+y[t]==Sqrt[2]*Sin[Sqrt[2]*t]; 
ic={y[0]==10,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 2 \sin (t)-\sqrt {2} \sin \left (\sqrt {2} t\right )+10 \cos (t) \end{align*}

✓ Sympy. Time used: 0.053 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t) - sqrt(2)*sin(sqrt(2)*t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 10, Subs(Derivative(y(t), t), t, 0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 2 \sin {\left (t \right )} - \sqrt {2} \sin {\left (\sqrt {2} t \right )} + 10 \cos {\left (t \right )} \]