72.13.1 problem 1

Internal problem ID [14862]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 3. Linear Systems. Exercises section 3.6 page 342
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 07:17:49 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }-7 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(diff(y(t),t$2)-6*diff(y(t),t)-7*y(t)=0,y(t), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{7 t}+c_{2} {\mathrm e}^{-t} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 22

DSolve[D[y[t],{t,2}]-6*D[y[t],t]-7*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-t} \left (c_2 e^{8 t}+c_1\right ) \]