Internal problem ID [5931]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 7 THE LAPLACE TRANSFORM. 7.3.1 TRANSLATION ON THE s-AXIS. Page
297
Problem number: 67.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y-\theta \left (-2 \pi +t \right ) \sin \relax (t )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.017 (sec). Leaf size: 28
dsolve([diff(y(t),t$2)+4*y(t)=sin(t)*Heaviside(t-2*Pi),y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = \cos \left (2 t \right )+\frac {\theta \left (-2 \pi +t \right ) \left (2 \sin \relax (t )-\sin \left (2 t \right )\right )}{6} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 32
DSolve[{y''[t]+4*y[t]==Sin[t]*UnitStep[t-2*Pi],{y[0]==1,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to {cc} \{ & {cc} \cos (2 t) & t\leq 2 \pi \\ \cos (2 t)-\frac {1}{3} (\cos (t)-1) \sin (t) & \text {True} \\ \\ \\ \\ \\ \end{align*}