73.18.4 problem 27.1 (d)

Internal problem ID [15588]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 27. Differentiation and the Laplace transform. Additional Exercises. page 496
Problem number : 27.1 (d)
Date solved : Tuesday, January 28, 2025 at 08:02:53 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y&=t^{3} \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 8.469 (sec). Leaf size: 25

dsolve([diff(y(t),t$2)-4*y(t)=t^3,y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = \frac {13 \,{\mathrm e}^{-2 t}}{32}-\frac {t^{3}}{4}-\frac {3 t}{8}+\frac {19 \,{\mathrm e}^{2 t}}{32} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 34

DSolve[{D[y[t],{t,2}]-4*y[t]==t^3,{y[0]==1,Derivative[1][y][0] ==3}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{32} \left (-4 t \left (2 t^2+3\right )-11 e^{-2 t}+43 e^{2 t}\right ) \]