52.5.8 problem 38

Internal problem ID [8331]
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 : 38
Date solved : Monday, January 27, 2025 at 03:49:07 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{t} \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.750 (sec). Leaf size: 21

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

\[ y = \frac {{\mathrm e}^{t}}{10}-\frac {\cos \left (3 t \right )}{10}-\frac {\sin \left (3 t \right )}{30} \]

✓ Solution by Mathematica

Time used: 0.129 (sec). Leaf size: 27

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

\[ y(t)\to \frac {1}{30} \left (3 e^t-\sin (3 t)-3 \cos (3 t)\right ) \]