15.11.22 problem 22

Internal problem ID [3132]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 19, page 86
Problem number : 22
Date solved : Sunday, March 30, 2025 at 01:19:10 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=\left (1+\sin \left (3 x \right )\right ) \cos \left (2 x \right ) \end{align*}

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

ode:=diff(diff(y(x),x),x)+9*y(x) = (1+sin(3*x))*cos(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sin \left (3 x \right ) c_2 +\cos \left (3 x \right ) c_1 +\frac {\cos \left (2 x \right )}{5}+\frac {\sin \left (x \right )}{16}-\frac {\sin \left (5 x \right )}{32} \]

✓ Mathematica. Time used: 0.152 (sec). Leaf size: 42

ode=D[y[x],{x,2}]+9*y[x]==(1+Sin[3*x])*Cos[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\sin (x)}{16}-\frac {1}{32} \sin (5 x)+\frac {1}{5} \cos (2 x)+c_1 \cos (3 x)+c_2 \sin (3 x) \]

✓ Sympy. Time used: 1.136 (sec). Leaf size: 105

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-sin(3*x) - 1)*cos(2*x) + 9*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{2} \cos {\left (3 x \right )} + \frac {\left (1 - \cos {\left (2 x \right )}\right )^{3} \sin {\left (x \right )}}{12} - \frac {\left (1 - \cos {\left (2 x \right )}\right )^{2} \sin {\left (x \right )}}{8} + \frac {\left (1 - \cos {\left (2 x \right )}\right )^{2} \sin {\left (5 x \right )}}{8} + \left (C_{1} + \frac {\left (1 - \cos {\left (2 x \right )}\right )^{3}}{4} - \frac {11 \left (1 - \cos {\left (2 x \right )}\right )^{2}}{24}\right ) \sin {\left (3 x \right )} + \frac {\sin {\left (x \right )}}{16} - \frac {\sin {\left (5 x \right )}}{4} + \frac {\sin {\left (7 x \right )}}{16} + \frac {\cos {\left (2 x \right )}}{5} \]