86.6.9 problem 9

Internal problem ID [23142]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 5. Linear equations of the second order with constant coefficients. Exercise 5b at page 77
Problem number : 9
Date solved : Thursday, October 02, 2025 at 09:23:26 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+8 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 28

ode:=diff(diff(y(x),x),x)-5*diff(y(x),x)+8*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\frac {5 x}{2}} \left (c_1 \sin \left (\frac {\sqrt {7}\, x}{2}\right )+c_2 \cos \left (\frac {\sqrt {7}\, x}{2}\right )\right ) \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 42

ode=D[y[x],{x,2}]-5*D[y[x],x]+8*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{5 x/2} \left (c_2 \cos \left (\frac {\sqrt {7} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {7} x}{2}\right )\right ) \end{align*}

✓ Sympy. Time used: 0.103 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(8*y(x) - 5*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} \sin {\left (\frac {\sqrt {7} x}{2} \right )} + C_{2} \cos {\left (\frac {\sqrt {7} x}{2} \right )}\right ) e^{\frac {5 x}{2}} \]