Internal problem ID [12497]
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: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=2 \left (\delta \left (x -1\right )\right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 28
dsolve([diff(y(x),x$2)-2*diff(y(x),x)+y(x)=2*Dirac(x-1),y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = 2 \operatorname {Heaviside}\left (x -1\right ) {\mathrm e}^{x -1} \left (x -1\right )+x \,{\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 24
DSolve[{y''[x]-2*y'[x]+y[x]==2*DiracDelta[x-1],{y[0]==0,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{x-1} (2 (x-1) \theta (x-1)+e x) \]