52.5.7 problem 37

Internal problem ID [8330]
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 : Monday, January 27, 2025 at 03:49:06 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*}

✓ Solution by Maple

Time used: 0.725 (sec). Leaf size: 24

dsolve([diff(y(t),t$2)+y(t)=sqrt(2)*sin(sqrt(2)*t),y(0) = 10, D(y)(0) = 0],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 29

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

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