8.7.2 problem 2

Internal problem ID [808]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 2
Date solved : Monday, January 27, 2025 at 03:08:58 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-9 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=15 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 17

dsolve([diff(y(x),x$2)-9*y(x)=0,y(0) = -1, D(y)(0) = 15],y(x), singsol=all)
 

\[ y = -3 \,{\mathrm e}^{-3 x}+2 \,{\mathrm e}^{3 x} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 20

DSolve[{D[y[x],{x,2}]-9*y[x]==0,{y[0]==-1,Derivative[1][y][0] ==15}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (2 e^{6 x}-3\right ) \]