Internal problem ID [11538]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 3, Laplace transform. Section 3.4 Impulsive sources. Exercises page
173
Problem number: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }+x=3 \left (\delta \left (-2 \pi +t \right )\right )} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([diff(x(t),t$2)+x(t)=3*Dirac(t-2*Pi),x(0) = 0, D(x)(0) = 1],x(t), singsol=all)
\[ x \left (t \right ) = \sin \left (t \right ) \left (3 \operatorname {Heaviside}\left (-2 \pi +t \right )+1\right ) \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 18
DSolve[{x''[t]+x[t]==3*DiracDelta[t-2*Pi],{x[0]==0,x'[0]==1}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to (3 \theta (t-2 \pi )+1) \sin (t) \]