Internal problem ID [2879]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth
edition, 2015
Section: Chapter 10, The Laplace Transform and Some Elementary Applications. Exercises for
10.7. page 704
Problem number: Problem 39.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-6 y=30 \operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{1-t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = -4] \end {align*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 45
dsolve([diff(y(t),t$2)+diff(y(t),t)-6*y(t)=30*Heaviside(t-1)*exp(-(t-1)),y(0) = 3, D(y)(0) = -4],y(t), singsol=all)
\[ y \left (t \right ) = \left ({\mathrm e}^{5 t}+3 \operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{3}+2 \operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{-2+5 t}-5 \operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{1+2 t}+2\right ) {\mathrm e}^{-3 t} \]
✓ Solution by Mathematica
Time used: 0.087 (sec). Leaf size: 66
DSolve[{y''[t]+y'[t]-6*y[t]==30*UnitStep[t-1]*Exp[-(t-1)],{y[0]==3,y'[0]==-4}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} e^{-3 t} \left (2+e^{5 t}\right ) & t\leq 1 \\ e^{-3 t-2} \left (2 e^2+3 e^5+2 e^{5 t}-5 e^{2 t+3}+e^{5 t+2}\right ) & \text {True} \\ \end {array} \\ \end {array} \]