46.6.14 problem 14

Internal problem ID [7360]
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 : 14
Date solved : Monday, January 27, 2025 at 02:50:58 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=50 t -100 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (2\right )&=-4\\ y^{\prime }\left (2\right )&=14 \end{align*}

✓ Solution by Maple

Time used: 0.223 (sec). Leaf size: 23

dsolve([diff(y(t),t$2)+2*diff(y(t),t)+5*y(t)=50*t-100,y(2) = -4, D(y)(2) = 14],y(t), singsol=all)
 

\[ y = 10 t -24+2 \sin \left (2 t -4\right ) {\mathrm e}^{-t +2} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 25

DSolve[{D[y[t],{t,2}]+2*D[y[t],t]+5*y[t]==50*t-100,{y[2]==-4,Derivative[1][y][2]==14}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 10 t-2 e^{2-t} \sin (4-2 t)-24 \]