64.1.9 problem 4(a)

Internal problem ID [13254]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 1, Differential equations and their solutions. Exercises page 13
Problem number : 4(a)
Date solved : Tuesday, January 28, 2025 at 05:13:16 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=0 \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)-2*diff(y(x),x)-8*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{-2 x}+c_{2} {\mathrm e}^{4 x} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 22

DSolve[D[y[x],{x,2}]-2*D[y[x],x]-8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (c_2 e^{6 x}+c_1\right ) \]