Internal problem ID [6699]
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. EXERCISES 7.5. Page 315
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\delta \left (t -2 \pi \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 1.953 (sec). Leaf size: 15
dsolve([diff(y(t),t$2)+y(t)=Dirac(t-2*Pi),y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t -2 \pi \right )+1\right ) \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 16
DSolve[{y''[t]+y[t]==DiracDelta[t-2*Pi],{y[0]==0,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to (\theta (t-2 \pi )+1) \sin (t) \]