Internal problem ID [2337]
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 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime }-2 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve([diff(y(t),t$2)+diff(y(t),t)-2*y(t)=0,y(0) = 1, D(y)(0) = 4],y(t), singsol=all)
\[ y \relax (t ) = 2 \,{\mathrm e}^{-2 t} {\mathrm e}^{3 t}-{\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 18
DSolve[{y''[t]+y'[t]-2*y[t]==0,{y[0]==1,y'[0]==4}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 2 e^t-e^{-2 t} \\ \end{align*}