58.11.16 problem 16

Internal problem ID [14747]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page 151
Problem number : 16
Date solved : Thursday, October 02, 2025 at 09:50:44 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} 2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=9 \,{\mathrm e}^{2 x}-8 \,{\mathrm e}^{3 x} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 30

ode:=diff(diff(diff(y(x),x),x),x)-2*diff(diff(y(x),x),x)-diff(y(x),x)+2*y(x) = 9*exp(2*x)-8*exp(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (3 x +c_3 -{\mathrm e}^{x}-4\right ) {\mathrm e}^{2 x}+c_1 \,{\mathrm e}^{x}+c_2 \,{\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 44

ode=D[y[x],{x,3}]-2*D[y[x],{x,2}]-D[y[x],x]+2*y[x]==9*Exp[2*x]-8*Exp[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -e^{3 x}+c_1 e^{-x}+\left (\frac {81}{32}+c_2\right ) e^x+e^{2 x} (3 x-4+c_3) \end{align*}

✓ Sympy. Time used: 0.169 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) + 8*exp(3*x) - 9*exp(2*x) - Derivative(y(x), x) - 2*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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