Internal problem ID [13909]
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 (k).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+9 y^{\prime }=\delta \left (t -1\right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0, y^{\prime \prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 5.234 (sec). Leaf size: 18
dsolve([diff(y(t),t$3)+9*diff(y(t),t)=Dirac(t-1),y(0) = 0, D(y)(0) = 0, (D@@2)(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {\operatorname {Heaviside}\left (t -1\right ) \left (-1+\cos \left (3 t -3\right )\right )}{9} \]
✓ Solution by Mathematica
Time used: 0.174 (sec). Leaf size: 21
DSolve[{y'''[t]+9*y'[t]==DiracDelta[t-1],{y[0]==0,y'[0]==0,y''[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {1}{9} \theta (t-1) (\cos (3-3 t)-1) \]