4.35 problem Problem 5(f)

Internal problem ID [10995]

Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section: Chapter 5.6 Laplace transform. Nonhomogeneous equations. Problems page 368
Problem number: Problem 5(f).
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]

\[ \boxed {y^{\prime \prime }-7 y^{\prime }+6 y-\left (\delta \left (-1+t \right )\right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 23

dsolve([diff(y(t),t$2)-7*diff(y(t),t)+6*y(t)=Dirac(t-1),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
 

\[ y \left (t \right ) = \frac {\operatorname {Heaviside}\left (t -1\right ) \left ({\mathrm e}^{-6+6 t}-{\mathrm e}^{t -1}\right )}{5} \]

Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 29

DSolve[{y''[t]-7*y'[t]+6*y[t]==DiracDelta[t-1],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \frac {1}{5} e^{t-6} \left (e^{5 t}-e^5\right ) \theta (t-1) \\ \end{align*}