73.21.5 problem 30.6 (e)

Internal problem ID [15624]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 30. Piecewise-defined functions and periodic functions. Additional Exercises. page 553
Problem number : 30.6 (e)
Date solved : Tuesday, January 28, 2025 at 08:03:16 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=\operatorname {Heaviside}\left (t -10\right ) \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: 8.965 (sec). Leaf size: 18

dsolve([diff(y(t),t$2)+9*y(t)=Heaviside(t-10),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = -\frac {\operatorname {Heaviside}\left (t -10\right ) \left (\cos \left (3 t -30\right )-1\right )}{9} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 26

DSolve[{D[y[t],{t,2}]+9*y[t]==UnitStep[t-10],{y[0]==0,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} \frac {2}{9} \sin ^2\left (15-\frac {3 t}{2}\right ) & t>10 \\ 0 & \text {True} \\ \end {array} \\ \end {array} \]