8.11.10 problem 10

Internal problem ID [878]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 10
Date solved : Tuesday, March 04, 2025 at 11:57:08 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=2 \cos \left (3 x \right )+3 \sin \left (3 x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 30

ode:=diff(diff(y(x),x),x)+9*y(x) = 2*cos(3*x)+3*sin(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-9 x +18 c_1 +2\right ) \cos \left (3 x \right )}{18}+\frac {\sin \left (3 x \right ) \left (x +3 c_2 \right )}{3} \]

✓ Mathematica. Time used: 0.167 (sec). Leaf size: 39

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

\[ y(x)\to \left (-\frac {x}{2}+\frac {1}{9}+c_1\right ) \cos (3 x)+\frac {1}{12} (4 x+1+12 c_2) \sin (3 x) \]

✓ Sympy. Time used: 0.118 (sec). Leaf size: 22

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

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