Internal problem ID [2370]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime }-6 y-30 \theta \left (t -1\right ) {\mathrm e}^{-t +1}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 3, y^{\prime }\relax (0) = -4] \end {align*}
✓ Solution by Maple
Time used: 0.031 (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)
\[ y \relax (t ) = \left ({\mathrm e}^{5 t}+2 \theta \left (t -1\right ) {\mathrm e}^{-2+5 t}-5 \theta \left (t -1\right ) {\mathrm e}^{1+2 t}+3 \theta \left (t -1\right ) {\mathrm e}^{3}+2\right ) {\mathrm e}^{-3 t} \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 59
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]
\begin{align*} y(t)\to {cc} \{ & {cc} e^{-3 t} \left (2+e^{5 t}\right ) & t\leq 1 \\ e^{-3 t} \left (2+3 e^3-5 e^{2 t+1}+e^{5 t-2} \left (2+e^2\right )\right ) & \text {True} \\ \\ \\ \\ \\ \end{align*}