73.15.2 problem 22.1 (b)

Internal problem ID [15354]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.1 (b)
Date solved : Thursday, March 13, 2025 at 05:55:52 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=27 \,{\mathrm e}^{6 x} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 21

ode:=diff(diff(y(x),x),x)-6*diff(y(x),x)+9*y(x) = 27*exp(6*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{3 x}+3 \,{\mathrm e}^{6 x} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 25

ode=D[y[x],{x,2}]-6*D[y[x],x]+9*y[x]==27*Exp[6*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{3 x} \left (3 e^{3 x}+c_2 x+c_1\right ) \]

✓ Sympy. Time used: 0.209 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) - 27*exp(6*x) - 6*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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