85.67.10 problem 10

Internal problem ID [22901]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 216
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:16:25 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }+16 y^{\prime \prime }&=64 \cos \left (4 x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 33

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+16*diff(diff(y(x),x),x) = 64*cos(4*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-c_1 -6\right ) \cos \left (4 x \right )}{16}+\frac {\left (-c_2 -8 x \right ) \sin \left (4 x \right )}{16}+c_3 x +c_4 \]

✓ Mathematica. Time used: 0.158 (sec). Leaf size: 38

ode=D[y[x],{x,4}]+16*D[y[x],{x,2}]==64*Cos[4*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_4 x-\frac {1}{16} (5+c_1) \cos (4 x)-\frac {1}{16} (8 x+c_2) \sin (4 x)+c_3 \end{align*}

✓ Sympy. Time used: 0.072 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-64*cos(4*x) + 16*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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