46.7.3 problem 20

Internal problem ID [7364]
Book : ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section : Chapter 6. Laplace Transforms. Problem set 6.3, page 224
Problem number : 20
Date solved : Monday, January 27, 2025 at 02:51:01 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+10 y^{\prime }+24 y&=144 t^{2} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&={\frac {19}{12}}\\ y^{\prime }\left (0\right )&=-5 \end{align*}

✓ Solution by Maple

Time used: 0.223 (sec). Leaf size: 14

dsolve([diff(y(t),t$2)+10*diff(y(t),t)+24*y(t)=144*t^2,y(0) = 19/12, D(y)(0) = -5],y(t), singsol=all)
 

\[ y = 6 t^{2}-5 t +\frac {19}{12} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 17

DSolve[{D[y[t],{t,2}]+10*D[y[t],t]+24*y[t]==144*t^2,{y[0]==19/12,Derivative[1][y][0] ==-5}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 6 t^2-5 t+\frac {19}{12} \]