46.6.11 problem 11

Internal problem ID [7357]
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 : 11
Date solved : Monday, January 27, 2025 at 02:50:56 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+\frac {9 y}{4}&=9 t^{3}+64 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&={\frac {63}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.240 (sec). Leaf size: 28

dsolve([diff(y(t),t$2)+3*diff(y(t),t)+225/100*y(t)=9*t^3+64,y(0) = 1, D(y)(0) = 63/2],y(t), singsol=all)
 

\[ y = 4 t^{3}+{\mathrm e}^{-\frac {3 t}{2}} t -16 t^{2}+{\mathrm e}^{-\frac {3 t}{2}}+32 t \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 28

DSolve[{D[y[t],{t,2}]+3*D[y[t],t]+225/100*y[t]==9*t^3+64,{y[0]==1,Derivative[1][y][0] ==315/10}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 4 t \left (t^2-4 t+8\right )+e^{-3 t/2} (t+1) \]