81.10.24 problem 14-24

Internal problem ID [21619]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 14. Second order homogeneous differential equations with constant coefficients. Page 297.
Problem number : 14-24
Date solved : Thursday, October 02, 2025 at 07:59:05 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }-3 y^{\prime }+18 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=diff(diff(diff(y(x),x),x),x)-4*diff(diff(y(x),x),x)-3*diff(y(x),x)+18*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 27

ode=D[y[x],{x,3}]-4*D[y[x],{x,2}]-3*D[y[x],x]+18*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-2 x} \left (e^{5 x} (c_3 x+c_2)+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.130 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(18*y(x) - 3*Derivative(y(x), x) - 4*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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