85.1.12 problem 5 (f)

Internal problem ID [22417]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. A Exercises at page 12
Problem number : 5 (f)
Date solved : Thursday, October 02, 2025 at 08:38:46 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=diff(diff(diff(y(x),x),x),x)-2*diff(diff(y(x),x),x)-5*diff(y(x),x)+6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_2 \,{\mathrm e}^{5 x}+c_3 \,{\mathrm e}^{3 x}+c_1 \right ) {\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 28

ode=D[y[x],{x,3}]-2*D[y[x],{x,2}]-5*D[y[x],{x,1}]+6*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{-2 x}+c_2 e^x+c_3 e^{3 x} \end{align*}

✓ Sympy. Time used: 0.099 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) - 5*Derivative(y(x), x) - 2*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 2 x} + C_{2} e^{x} + C_{3} e^{3 x} \]