Internal problem ID [14449]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.1, page 141
Problem number: 13.
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 ) = -5] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 15
dsolve([diff(y(t),t$2)-diff(y(t),t)-2*y(t)=0,y(0) = -1, D(y)(0) = -5],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-t}-2 \,{\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 18
DSolve[{y''[t]-y'[t]-2*y[t]==0,{y[0]==-1,y'[0]==-5}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-t}-2 e^{2 t} \]