15.9.18 problem 32

Internal problem ID [3075]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 17, page 78
Problem number : 32
Date solved : Sunday, March 30, 2025 at 01:18:02 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-9 y^{\prime \prime }+23 y^{\prime }-15 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

ode:=diff(diff(diff(y(x),x),x),x)-9*diff(diff(y(x),x),x)+23*diff(y(x),x)-15*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} \left (c_1 +c_2 \,{\mathrm e}^{2 x}+c_3 \,{\mathrm e}^{4 x}\right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 28

ode=D[y[x],{x,3}]-9*D[y[x],{x,2}]+23*D[y[x],x]-15*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^x \left (c_2 e^{2 x}+c_3 e^{4 x}+c_1\right ) \]

✓ Sympy. Time used: 0.173 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-15*y(x) + 23*Derivative(y(x), x) - 9*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{2} e^{2 x} + C_{3} e^{4 x}\right ) e^{x} \]