46.8.10 problem 12

Internal problem ID [7381]
Book : ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section : Chapter 6. Laplace Transforms. Problem set 6.4, page 230
Problem number : 12
Date solved : Monday, January 27, 2025 at 02:51:24 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=25 t -100 \delta \left (t -\pi \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: 0.280 (sec). Leaf size: 27

dsolve([diff(y(t),t$2)+2*diff(y(t),t)+5*y(t)=25*t-100*Dirac(t-Pi),y(0) = -2, D(y)(0) = 5],y(t), singsol=all)
 

\[ y = -50 \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right ) {\mathrm e}^{\pi -t}+5 t -2 \]

✓ Solution by Mathematica

Time used: 0.258 (sec). Leaf size: 29

DSolve[{D[y[t],{t,2}]+2*D[y[t],t]+5*y[t]==25*t-100*DiracDelta[t-Pi],{y[0]==-2,Derivative[1][y][0] ==5}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -50 e^{\pi -t} \theta (t-\pi ) \sin (2 t)+5 t-2 \]