Internal problem ID [12496]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 5. The Laplace Transform Method. Exercises 5.5, page 273
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y=\delta \left (x -\pi \right )+\delta \left (x -3 \pi \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 23
dsolve([diff(y(x),x$2)+9*y(x)=Dirac(x-Pi)+Dirac(x-3*Pi),y(0) = 0, D(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (\operatorname {Heaviside}\left (x -3 \pi \right )+\operatorname {Heaviside}\left (x -\pi \right )\right ) \sin \left (3 x \right )}{3} \]
✓ Solution by Mathematica
Time used: 0.085 (sec). Leaf size: 26
DSolve[{y''[x]+9*y[x]==DiracDelta[x-Pi]+DiracDelta[x-3*Pi],{y[0]==0,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{3} (\theta (x-3 \pi )+\theta (x-\pi )) \sin (3 x) \]