Internal problem ID [12494]
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: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+3 y=\delta \left (x -2\right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 20
dsolve([diff(y(x),x)+3*y(x)=Dirac(x-2),y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {Heaviside}\left (x -2\right ) {\mathrm e}^{6-3 x}+{\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 21
DSolve[{y'[x]+3*y[x]==DiracDelta[x-2],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x} \left (e^6 \theta (x-2)+1\right ) \]