8.11.22 problem 45

Internal problem ID [890]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 45
Date solved : Tuesday, March 04, 2025 at 11:59:36 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=\sin \left (x \right )^{4} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 32

ode:=diff(diff(y(x),x),x)+9*y(x) = sin(x)^4; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sin \left (3 x \right ) c_2 +\cos \left (3 x \right ) c_1 -\frac {\cos \left (2 x \right )}{10}-\frac {\cos \left (2 x \right )^{2}}{28}+\frac {5}{84} \]

✓ Mathematica. Time used: 0.043 (sec). Leaf size: 39

ode=D[y[x],{x,2}]+9*y[x]==Sin[x]^4; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {1}{10} \cos (2 x)-\frac {1}{56} \cos (4 x)+c_1 \cos (3 x)+c_2 \sin (3 x)+\frac {1}{24} \]

✓ Sympy. Time used: 2.301 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) - sin(x)**4 + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sin {\left (3 x \right )} + C_{2} \cos {\left (3 x \right )} - \frac {\left (1 - \cos {\left (2 x \right )}\right )^{2}}{28} - \frac {6 \cos {\left (2 x \right )}}{35} + \frac {2}{21} \]