Internal problem ID [13588]
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 (j).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-12 y^{\prime }+45 y=\delta \left (t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 14
dsolve([diff(y(t),t$2)-12*diff(y(t),t)+45*y(t)=Dirac(t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {{\mathrm e}^{6 t} \sin \left (3 t \right )}{3} \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 25
DSolve[{y''[t]-12*y'[t]+45*y[t]==DiracDelta[t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {1}{3} e^{6 t} (\theta (0)-\theta (t)) \sin (3 t) \]