1.11.28 problem 28

Internal problem ID [349]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 28
Date solved : Tuesday, September 30, 2025 at 03:57:39 AM
CAS classification : [[_high_order, _missing_y]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 41

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

\[ y = \frac {\left (6 x^{3}-108 c_1 +x \right ) \cos \left (3 x \right )}{972}+\frac {\left (-45 x^{2}-324 c_2 -11\right ) \sin \left (3 x \right )}{2916}+c_3 x +c_4 \]

✓ Mathematica. Time used: 0.476 (sec). Leaf size: 51

ode=D[y[x],{x,4}]+9*D[y[x],{x,2}]==(x^2+1)*Sin[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {6 \left (6 x^3+x-108 c_1\right ) \cos (3 x)-\left (90 x^2+41+648 c_2\right ) \sin (3 x)}{5832}+c_4 x+c_3 \end{align*}

✓ Sympy. Time used: 0.161 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-x**2 - 1)*sin(3*x) + 9*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + x \left (C_{2} + \frac {\cos {\left (3 x \right )}}{972}\right ) + \left (C_{3} - \frac {5 x^{2}}{324}\right ) \sin {\left (3 x \right )} + \left (C_{4} + \frac {x^{3}}{162}\right ) \cos {\left (3 x \right )} \]