67.15.13 problem 22.5 (c)

Internal problem ID [16731]
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 : 22.5 (c)
Date solved : Thursday, October 02, 2025 at 01:38:16 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=18 x^{2}+3 x +4 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)-6*diff(y(x),x)+9*y(x) = 18*x^2+3*x+4; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 32

ode=D[y[x],{x,2}]-6*D[y[x],x]+9*y[x]==18*x^2+3*x+4; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 x^2+x \left (3+c_2 e^{3 x}\right )+c_1 e^{3 x}+2 \end{align*}

✓ Sympy. Time used: 0.114 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-18*x**2 - 3*x + 9*y(x) - 6*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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