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 : Tuesday, March 04, 2025 at 11:06:44 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*}

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

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)-5*y(x) = 0; 
ic:=y(0) = 1, D(y)(0) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.212 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-5*y(x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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