Internal problem ID [13587]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 31. Delta Functions. Additional Exercises. page 572
Problem number: 31.7 (i).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+9 y=\delta \left (t -4\right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 18
dsolve([diff(y(t),t$2)+6*diff(y(t),t)+9*y(t)=Dirac(t-4),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \left (t -4\right ) {\mathrm e}^{-3 t +12} \operatorname {Heaviside}\left (t -4\right ) \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 20
DSolve[{y''[t]+6*y'[t]+9*y[t]==DiracDelta[t-4],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{12-3 t} (t-4) \theta (t-4) \]