67.15.17 problem 22.7 (b)

Internal problem ID [16735]
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 : 22.7 (b)
Date solved : Thursday, October 02, 2025 at 01:38:19 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{2 x} \sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)-6*diff(y(x),x)+9*y(x) = exp(2*x)*sin(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.055 (sec). Leaf size: 57

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

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

✓ Sympy. Time used: 0.186 (sec). Leaf size: 20

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

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