Internal problem ID [12495]
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: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }-3 y=\delta \left (x -1\right )+2 \operatorname {Heaviside}\left (x -2\right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 46
dsolve([diff(y(x),x)-3*y(x)=Dirac(x-1)+2*Heaviside(x-2),y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {2 \operatorname {Heaviside}\left (x -2\right )}{3}+\frac {2 \operatorname {Heaviside}\left (x -2\right ) {\mathrm e}^{-6+3 x}}{3}+\operatorname {Heaviside}\left (x -1\right ) {\mathrm e}^{3 x -3} \]
✓ Solution by Mathematica
Time used: 0.212 (sec). Leaf size: 44
DSolve[{y'[x]-3*y[x]==DiracDelta[x-1]+2*UnitStep[x-2],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{3 x-3} \theta (x-1)+\frac {2 \left (e^6-e^{3 x}\right ) (\theta (2-x)-1)}{3 e^6} \]