Internal problem ID [14057]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-12 y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve(diff(y(t),t$2)-diff(y(t),t)-12*y(t)=0,y(t), singsol=all)
\[ y \left (t \right ) = \left ({\mathrm e}^{7 t} c_{2} +c_{1} \right ) {\mathrm e}^{-3 t} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 22
DSolve[y''[t]-y'[t]-12*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-3 t} \left (c_2 e^{7 t}+c_1\right ) \]