7.9.15 problem 31(b)

Internal problem ID [263]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.2 (General solutions of linear equations). Problems at page 122
Problem number : 31(b)
Date solved : Monday, January 27, 2025 at 02:43:06 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-5 y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 36

dsolve([diff(y(x),x$2)-2*diff(y(x),x)-5*y(x)=0,y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
 

\[ y = \frac {\left (6+\sqrt {6}\right ) {\mathrm e}^{-\left (-1+\sqrt {6}\right ) x}}{12}-\frac {{\mathrm e}^{\left (1+\sqrt {6}\right ) x} \left (\sqrt {6}-6\right )}{12} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 47

DSolve[{D[y[x],{x,2}]-2*D[y[x],x]-5*y[x]==0,{y[0]==1,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{12} e^{x-\sqrt {6} x} \left (-\left (\sqrt {6}-6\right ) e^{2 \sqrt {6} x}+6+\sqrt {6}\right ) \]