81.14.14 problem 18-27

Internal problem ID [21699]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 18. Algebra of differential operators. Page 435
Problem number : 18-27
Date solved : Thursday, October 02, 2025 at 08:00:07 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+3 y^{\prime }+9 y&={\mathrm e}^{3 x} \end{align*}

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

ode:=diff(diff(diff(y(x),x),x),x)-5*diff(diff(y(x),x),x)+3*diff(y(x),x)+9*y(x) = exp(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (8 c_3 x +x^{2}+8 c_2 \right ) {\mathrm e}^{3 x}}{8}+c_1 \,{\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 41

ode=D[y[x],{x,3}]-5*D[y[x],{x,2}]+3*D[y[x],x]+9*y[x]==Exp[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{3 x} \left (\frac {x^2}{8}+\left (-\frac {1}{16}+c_3\right ) x+\frac {1}{64}+c_2\right )+c_1 e^{-x} \end{align*}

✓ Sympy. Time used: 0.178 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) - exp(3*x) + 3*Derivative(y(x), x) - 5*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{3} e^{- x} + \left (C_{1} + x \left (C_{2} + \frac {x}{8}\right )\right ) e^{3 x} \]