Internal problem ID [13590]
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 (L).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }-16 y=\delta \left (t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0, y^{\prime \prime }\left (0\right ) = 0, y^{\prime \prime \prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 17
dsolve([diff(y(t),t$4)-16*y(t)=Dirac(t),y(0) = 0, D(y)(0) = 0, (D@@2)(y)(0) = 0, (D@@3)(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {\sin \left (2 t \right )}{16}+\frac {\sinh \left (2 t \right )}{16} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 39
DSolve[{y''''[t]-16*y[t]==DiracDelta[t],{y[0]==0,y'[0]==0,y''[0]==0,y'''[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {1}{32} e^{-2 t} (\theta (0)-\theta (t)) \left (e^{4 t}-2 e^{2 t} \sin (2 t)-1\right ) \]