Internal problem ID [2341]
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 10.4.
page 689
Problem number: Problem 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime }-2 y-10 \,{\mathrm e}^{-t}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.019 (sec). Leaf size: 21
dsolve([diff(y(t),t$2)+diff(y(t),t)-2*y(t)=10*exp(-t),y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = \left (2 \,{\mathrm e}^{3 t}-5 \,{\mathrm e}^{t}+3\right ) {\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 25
DSolve[{y''[t]+y'[t]-2*y[t]==10*Exp[-t],{y[0]==0,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-2 t} \left (-5 e^t+2 e^{3 t}+3\right ) \\ \end{align*}