67.15.70 problem 22.14 (a)

Internal problem ID [16788]
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 : 22.14 (a)
Date solved : Thursday, October 02, 2025 at 01:38:51 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=27 \,{\mathrm e}^{6 x}+25 \sin \left (6 x \right ) \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 33

ode:=diff(diff(y(x),x),x)-6*diff(y(x),x)+9*y(x) = 27*exp(6*x)+25*sin(6*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 x +c_2 \right ) {\mathrm e}^{3 x}+\frac {4 \cos \left (6 x \right )}{9}+3 \,{\mathrm e}^{6 x}-\frac {\sin \left (6 x \right )}{3} \]

✓ Mathematica. Time used: 0.355 (sec). Leaf size: 82

ode=D[y[x],{x,2}]-6*D[y[x],x]+9*y[x]==27*Exp[6*x]+25*Sin[6*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{3 x} \left (\int _1^x-e^{-3 K[1]} K[1] \left (25 \sin (6 K[1])+27 e^{6 K[1]}\right )dK[1]+x \int _1^x\left (25 e^{-3 K[2]} \sin (6 K[2])+27 e^{3 K[2]}\right )dK[2]+c_2 x+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.184 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) - 27*exp(6*x) - 25*sin(6*x) - 6*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{2} x\right ) e^{3 x} + 3 e^{6 x} - \frac {\sin {\left (6 x \right )}}{3} + \frac {4 \cos {\left (6 x \right )}}{9} \]