78.1.46 problem 6

Internal problem ID [18030]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 6
Date solved : Monday, March 31, 2025 at 04:57:16 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

ode:=diff(diff(y(x),x),x)-5*diff(y(x),x)+6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{x}+c_2 \right ) {\mathrm e}^{2 x} \]

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

ode=D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.140 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) - 5*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{2} e^{x}\right ) e^{2 x} \]