8.7.6 problem 6

Internal problem ID [812]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 6
Date solved : Monday, January 27, 2025 at 03:09:07 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=7\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 17

dsolve([diff(y(x),x$2)+diff(y(x),x)-6*y(x)=0,y(0) = 7, D(y)(0) = -1],y(x), singsol=all)
 

\[ y = \left (4 \,{\mathrm e}^{5 x}+3\right ) {\mathrm e}^{-3 x} \]

✓ Solution by Mathematica

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

DSolve[{D[y[x],{x,2}]+D[y[x],x]-6*y[x]==0,{y[0]==7,Derivative[1][y][0] ==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (4 e^{5 x}+3\right ) \]