73.19.2 problem 28.6 (b)

Internal problem ID [15600]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 28. The inverse Laplace transform. Additional Exercises. page 509
Problem number : 28.6 (b)
Date solved : Tuesday, January 28, 2025 at 08:03:01 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=27 t^{3} \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 7.902 (sec). Leaf size: 19

dsolve([diff(y(t),t$2)+9*y(t)=27*t^3,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = 3 t^{3}+\frac {2 \sin \left (3 t \right )}{3}-2 t \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 22

DSolve[{D[y[t],{t,2}]+9*y[t]==27*t^3,{y[0]==0,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 3 t^3-2 t+\frac {2}{3} \sin (3 t) \]