Internal problem ID [2846]
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]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-2 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 1.75 (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)
\[ y \left (t \right ) = \left (2 \,{\mathrm e}^{3 t}-1\right ) {\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 18
DSolve[{y''[t]+y'[t]-2*y[t]==0,{y[0]==1,y'[0]==4}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 2 e^t-e^{-2 t} \]