58.11.54 problem 54

Internal problem ID [14785]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page 151
Problem number : 54
Date solved : Thursday, October 02, 2025 at 09:54:51 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y&=\sin \left (2 x \right ) \sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 45

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+10*diff(diff(y(x),x),x)+9*y(x) = sin(x)*sin(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (11+1152 c_3 \right ) \cos \left (3 x \right )}{1152}+\frac {\left (x +96 c_4 \right ) \sin \left (3 x \right )}{96}+\frac {\left (-1+64 c_1 \right ) \cos \left (x \right )}{64}+\frac {\sin \left (x \right ) \left (x +32 c_2 \right )}{32} \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 54

ode=D[y[x],{x,4}]+10*D[y[x],{x,2}]+9*y[x]==Sin[x]*Sin[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{32} x \sin (x)+\frac {1}{96} x \sin (3 x)+\left (-\frac {1}{64}+c_3\right ) \cos (x)+\left (\frac {13}{576}+c_1\right ) \cos (3 x)+c_4 \sin (x)+c_2 \sin (3 x) \end{align*}

✓ Sympy. Time used: 1.264 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) - sin(x)*sin(2*x) + 10*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{3} \cos {\left (x \right )} + C_{4} \cos {\left (3 x \right )} + \left (C_{1} + \frac {x}{96}\right ) \sin {\left (3 x \right )} + \left (C_{2} + \frac {x}{32}\right ) \sin {\left (x \right )} \]