Internal problem ID [863]
Book: Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima,
Meade
Section: Chapter 6.5, The Laplace Transform. Impulse functions. page 273
Problem number: 8.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }-y-\left (\delta \left (t -1\right )\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 0, y^{\prime \prime }\relax (0) = 0, y^{\prime \prime \prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 29
dsolve([diff(y(t),t$4)-y(t)=Dirac(t-1),y(0) = 0, D(y)(0) = 0, (D@@2)(y)(0) = 0, (D@@3)(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = -\frac {\theta \left (t -1\right ) \left (-{\mathrm e}^{t -1}+{\mathrm e}^{-t +1}+2 \sin \left (t -1\right )\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 28
DSolve[{y''''[t]-y[t]==DiracDelta[t-1],{y[0]==0,y'[0]==0,y''[0]==0,y'''[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{2} \theta (t-1) (\sin (1-t)-\sinh (1-t)) \\ \end{align*}