Internal problem ID [10977]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 5.6 Laplace transform. Nonhomogeneous equations. Problems page 368
Problem number: Problem 3(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y-24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 19
dsolve([diff(y(t),t$2)+9*y(t)=24*sin(t)*(Heaviside(t)+Heaviside(t-Pi)),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = 4 \sin \left (t \right )^{3} \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 24
DSolve[{y''[t]+9*y[t]==24*Sin[t]*(UnitStep[t]+UnitStep[t-Pi]),{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 4 (\theta (\pi -t) (\theta (t)-2)+2) \sin ^3(t) \\ \end{align*}