52.7.3 problem 11

Internal problem ID [8358]
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. 7.4.1 DERIVATIVES OF A TRANSFORM. Page 309
Problem number : 11
Date solved : Monday, January 27, 2025 at 03:49:30 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=\cos \left (3 t \right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=5 \end{align*}

✓ Solution by Maple

Time used: 0.593 (sec). Leaf size: 20

dsolve([diff(y(t),t$2)+9*y(t)=cos(3*t),y(0) = 2, D(y)(0) = 5],y(t), singsol=all)
 

\[ y = 2 \cos \left (3 t \right )+\frac {\sin \left (3 t \right ) \left (10+t \right )}{6} \]

✓ Solution by Mathematica

Time used: 0.072 (sec). Leaf size: 23

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

\[ y(t)\to \frac {1}{6} (t+10) \sin (3 t)+2 \cos (3 t) \]