8.11.30 problem 53

Internal problem ID [898]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 53
Date solved : Tuesday, March 04, 2025 at 12:00:03 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 33

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

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 39

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

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

✓ Sympy. Time used: 0.259 (sec). Leaf size: 31

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

\[ y{\left (x \right )} = \left (C_{1} + \frac {2 x}{3}\right ) \sin {\left (3 x \right )} + \left (C_{2} + \frac {2 \log {\left (\cos {\left (3 x \right )} \right )}}{9}\right ) \cos {\left (3 x \right )} \]