Internal problem ID [6710]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 7 THE LAPLACE TRANSFORM. EXERCISES 7.5. Page 315
Problem number: 15(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+10 y=\delta \left (t \right )} \]
✓ Solution by Maple
Time used: 1.86 (sec). Leaf size: 30
dsolve(diff(y(t),t$2)+2*diff(y(t),t)+10*y(t)=Dirac(t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {{\mathrm e}^{-t} \left (3 y \left (0\right ) \cos \left (3 t \right )+\sin \left (3 t \right ) \left (D\left (y \right )\left (0\right )+y \left (0\right )+1\right )\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.062 (sec). Leaf size: 38
DSolve[y''[t]+2*y'[t]+10*y[t]==DiracDelta[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{3} e^{-t} (\theta (t) \sin (3 t)+3 c_2 \cos (3 t)+3 c_1 \sin (3 t)) \]