46.6.10 problem 10

Internal problem ID [7356]
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 : 10
Date solved : Monday, January 27, 2025 at 02:50:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+\frac {y}{25}&=\frac {t^{2}}{50} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=-25\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.227 (sec). Leaf size: 11

dsolve([diff(y(t),t$2)+4/100*y(t)=2/100*t^2,y(0) = -25, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = \frac {t^{2}}{2}-25 \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 14

DSolve[{D[y[t],{t,2}]+4/100*y[t]==2/100*t^2,{y[0]==-25,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{2} \left (t^2-50\right ) \]