73.17.5 problem 5

Internal problem ID [15468]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 5
Date solved : Monday, March 31, 2025 at 01:38:46 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-9 y^{\prime }+14 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)-9*diff(y(x),x)+14*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{5 x}+c_2 \right ) {\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 22

ode=D[y[x],{x,2}]-9*D[y[x],x]+14*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{2 x} \left (c_2 e^{5 x}+c_1\right ) \]

✓ Sympy. Time used: 0.152 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(14*y(x) - 9*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{2} e^{5 x}\right ) e^{2 x} \]