15.9.24 problem 38

Internal problem ID [3081]
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 : 38
Date solved : Sunday, March 30, 2025 at 01:18:07 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }-2 y^{\prime }+24 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=diff(diff(diff(y(x),x),x),x)-5*diff(diff(y(x),x),x)-2*diff(y(x),x)+24*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_3 \,{\mathrm e}^{6 x}+c_1 \,{\mathrm e}^{5 x}+c_2 \right ) {\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 29

ode=D[y[x],{x,3}]-5*D[y[x],{x,2}]-2*D[y[x],x]+24*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.173 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(24*y(x) - 2*Derivative(y(x), x) - 5*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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