46.6.4 problem 4

Internal problem ID [7350]
Book : ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section : Chapter 6. Laplace Transforms. Problem set 6.2, page 216
Problem number : 4
Date solved : Monday, January 27, 2025 at 02:50:52 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+9 y&=10 \,{\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: 0.266 (sec). Leaf size: 21

dsolve([diff(y(t),t$2)+9*y(t)=10*exp(-t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 25

DSolve[{D[y[t],{t,2}]+9*y[t]==10*Exp[-t],{y[0]==0,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

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